Best Answer

By factoring or by completing the the square.

Factoring:

x2-3x = 0

x(x-3) = 0

So x = 0 or x = 3

Completing the square:

x2-3x = 0

(x-1.5)2 = 0

(x-1.5)2 - 2.25 = 0

(x-1.5)2 = 2.25

x-1.5 = + or - the square root of 2.25 (which is 1.5)

x = 1.5 + or - 1.5

So x = 0 or x = 3

Q: How can you solve quadratic equations without constant for example x2-3x equals 0?

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Why Do We Study Quadratic Equation?In maths class, we are hammered with expressions after expressions of quadratic equations. We are taught how to solve for its roots. We are taught all the necessary methods or mathematical techniques to handle quadratic equations. But after all these, what is the purpose?This is the question many students of maths studies ask.Do we need this "quadratic" knowledge in working life?The communication dish is parabolic in shape. Parabolic is the equivalent to quadratic mathematically. Engineers need to understand quadratic equation to design this beautiful profile.the pan is a wok that is designed using quadratic expression. With this, food can be fried to our liking!Without quadratic equation, who knows how a wok would look like.eye-glass lens are constructed with curves matching that of the quadratic equation.Light is thus controlled to give good image to our eyes.Quadratic equations to the rescue, right?Other examplesare:1) Distance travelled given by the quadratic equation s = ut + (1/2) a t22) Electrical characteristics of a MOSFET (Transistor device)i = k [(Vg - Vt)VD - (1/2)Vd2]So now do you still wonder why you study quadratic equations?with out math these things wouldn't have existed then their would be no dish that will connect us to channels all over the world or like food how can we eat without a pan or even lenses, we all study math for a purpose and it's not just to pass an exam, it's to know more knowledge about whats around us

There are 5 existing methods in solving quadratic equations. For the first 4 methods (quadratic formula, factoring, graphing, completing the square) you can easily find them in algebra books. I would like to explain here the new one, the Diagonal Sum Method, recently presented in book titled:"New methods for solving quadratic equations and inequalities" (Trafford 2009). It directly gives the 2 roots in the form of 2 fractions, without having to factor the equation. The innovative concept of the method is finding 2 fractions knowing their Sum (-b/a) and their Product (c/a). It is very fast, convenient and is applicable whenever the given quadratic equation is factorable. In general, it is hard to tell in advance if a given quadratic equation can be factored. However, if this new method fails to find the answer, then we can conclude that the equation can not be factored, and consequently, the quadratic formula must be used. This new method can replace the trial-and-error factoring method since it is faster, more convenient, with fewer permutations and fewer trials.

An equation just has an equal sign. A function is basically just an equation without one!

A constant in an algebraic expression is a number that does not change. For example x + 2 The 2 is a constant (does not change) x is a variable (can take on any value)

Pretend C is 0 (zero)

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Why Do We Study Quadratic Equation?In maths class, we are hammered with expressions after expressions of quadratic equations. We are taught how to solve for its roots. We are taught all the necessary methods or mathematical techniques to handle quadratic equations. But after all these, what is the purpose?This is the question many students of maths studies ask.Do we need this "quadratic" knowledge in working life?The communication dish is parabolic in shape. Parabolic is the equivalent to quadratic mathematically. Engineers need to understand quadratic equation to design this beautiful profile.the pan is a wok that is designed using quadratic expression. With this, food can be fried to our liking!Without quadratic equation, who knows how a wok would look like.eye-glass lens are constructed with curves matching that of the quadratic equation.Light is thus controlled to give good image to our eyes.Quadratic equations to the rescue, right?Other examplesare:1) Distance travelled given by the quadratic equation s = ut + (1/2) a t22) Electrical characteristics of a MOSFET (Transistor device)i = k [(Vg - Vt)VD - (1/2)Vd2]So now do you still wonder why you study quadratic equations?with out math these things wouldn't have existed then their would be no dish that will connect us to channels all over the world or like food how can we eat without a pan or even lenses, we all study math for a purpose and it's not just to pass an exam, it's to know more knowledge about whats around us

There are 5 existing methods in solving quadratic equations. For the first 4 methods (quadratic formula, factoring, graphing, completing the square) you can easily find them in algebra books. I would like to explain here the new one, the Diagonal Sum Method, recently presented in book titled:"New methods for solving quadratic equations and inequalities" (Trafford 2009). It directly gives the 2 roots in the form of 2 fractions, without having to factor the equation. The innovative concept of the method is finding 2 fractions knowing their Sum (-b/a) and their Product (c/a). It is very fast, convenient and is applicable whenever the given quadratic equation is factorable. In general, it is hard to tell in advance if a given quadratic equation can be factored. However, if this new method fails to find the answer, then we can conclude that the equation can not be factored, and consequently, the quadratic formula must be used. This new method can replace the trial-and-error factoring method since it is faster, more convenient, with fewer permutations and fewer trials.

Automatically. What type of equations.

Police, Quadratics, Action! If you know the initial speed of car, how far you are travelling and what your acceleration is, there is a special formula that lets you find out how long the journey will take. This formula is a quadratic with time as its unknown quadratic quantity. The police use this equation - along with many other quadratic and non-quadratic equations - when they attend a road traffic accident (RTA). They do this to find out if the driver was breaking the speed limit or driving without due care and attention. They can discover how fast the car was going at the time the driver started braking and how long they were braking for before they had the accident. This is done by finding the road's coefficient of friction and by measuring the length of the skid marks of the vehicles involved. Once they have this information they turn to Mathematics and the trusted quadratic equation. Einstein's Famous Quadratic The most famous equation in the world is technically quadratic. Einstein discovered the formula: Where E is the Energy of an object, m is its mass and c is the speed of light. This formula relates mass and energy and came from Einstein's work on Special and General Relativity. However, in practice it is not solved as a quadratic equation as we know the value of the speed of light. For more information on Einstein and his Theory of Special Relativity see the links at the bottom of the page. There are many more uses for quadratic equations. For more information please see the links to "101 Uses of a Quadratic Equation" at the bottom of the page.

The standard form of a quadratic equation is: ax^2 + bx + c = 0. Depending on the values of the constants (a, b, and c), a quadratic equation may have 2 real roots, one double roots, or no real roots.There are many "special cases" of quadratic equations.1. When a = 1, the equation is in the form: x^2 + bx + c = 0. Solving it becomes solving a popular puzzle: find 2 numbers knowing their sum (-b) and their product (c). If you use the new Diagonal Sum Method (Amazon e-book 2010), solving is fast and simple.Example: Solve x^2 + 33x - 108 = 0.Solution. Roots have opposite signs. Write factor pairs of c = -108. They are: (-1, 108),(-2, 54),(-3, 36)...This sum is -3 + 36 = 33 = -b. The 2 real roots are -3 and 36. There is no needs for factoring.2. Tips for solving 2 special cases of quadratic equations.a. When a + b + c = 0, one real root is (1) and the other is (c/a).Example: the equation 5x^2 - 7x + 2 = 0 has 2 real roots: 1 and 2/5b. When a - b + c = 0, one real roots is (-1) and the other is (-c/a)Example: the equation 6x^2 - 3x - 9 = 0 has 2 real roots: (-1) and (9/6).3. Quadratic equations that can be factored.The standard form of a quadratic equation is ax^2 + bx + c = 0. When the Discriminant D = b^2 - 4ac is a perfect square, this equation can be factored into 2 binomials in x: (mx + n)(px + q)= 0. Solving the quadratic equation results in solving these 2 binomials for x. Students should master how to use this factoring method instead of boringly using the quadratic formula.When a given quadratic equation can be factored, there are 2 best solving methods to choose:a. The "factoring ac method" (You Tube) that determines the values of the constants m, n, p, and q of the 2 above mentioned binomials in x.b. The Diagonal Sum Method (Amazon ebook 2010) that directly obtains the 2 real roots without factoring. It is also considered as "The c/a method", or the shortcut of the factoring method. See the article titled" Solving quadratic equations by the Diagonal Sum Method" on this website.4. Quadratic equations that have 2 roots in the form of 2 complex numbers.When the Discriminant D = b^2 - 4ac < 0, there are 2 roots in the form of 2 complex numbers.5. Some special forms of quadratic equations:- quadratic equations with parameters: x^2 + mx - 7 + 0 (m is a parameter)- bi-quadratic equations: x^4 - 5x^2 + 4 = 0- equations with rational expression: (ax + b)/(cx + d) = (ex + f)- equations with radical expressions.

There is a new method, called Diagonal Sum Method, that quickly and directly give the 2 roots without having to factor the equation. The innovative concept of this method is finding 2 fractions knowing their sum (-b/a) and their product (c/a). It is fast, convenient and is applicable to any quadratic equation in standard form ax^2 + bx + c = 0, whenever it can be factored. If it fails to find answer, then the equation is not factorable, and consequently, the quadratic formula must be used. So, I advise you to proceed solving any quadratic equation in 2 steps. First, find out if the equation can be factored? How?. Use this new method to solve it. It usually takes fewer than 3 trials. If its fails then use the quadratic formula to solve it in the second step. See book titled:" New methods for solving quadratic equations and inequalities" (Trafford Publishing 2009)

using the quadratic formula or the graphics calculator. Yes, you can do it another way, by using a new method, called Diagonal Sum Method, that can quickly and directly give the 2 roots, without having to factor the equation. This method is fast, convenient and is applicable to any quadratic equation in standard form ax^2 +bx + c = 0, whenever it can be factored. It requires fewer permutations than the factoring method does, especially when the constants a, b, and c are large numbers. If this method fails to get answer, then consequently, the quadratic formula must be used to solve the given equation. It is a trial-and-error method, same as the factoring method, that usually takes fewer than 3 trials to solve any quadratic equation. See book titled:" New methods for solving quadratic equations and inequalities" (Trafford Publishing 2009)

A constant in an algebraic expression is a number that does not change. For example x + 2 The 2 is a constant (does not change) x is a variable (can take on any value)

Square :)

Finally, there are two methods to use, depending on if the given quadratic equation can be factored or not. 1.- The first one is the new Diagonal Sum Method, recently presented in book titled: "New methods for solving quadratic equations" (Trafford 2009). This method directly gives the two roots in the form of two fractions, without having to factor it. The innovative concept of this new method is finding 2 fractions knowing their product (c/a) and their sum (-b/a). This new method is applicable to any quadratic equation that can be factored. It can replace the existing trial-and-error factoring method since this last one contains too many more permutations. In general, it is hard to tell in advance if a given quadratic equation can be factored. However, if the new method fails to get the answers, then you can positively conclude that this equation can not be factored. Consequently, the quadratic formula must be used in solving. We advise students to always try to solve the given equation by the new method first. If the student gets conversant with this method, it usually take less than 2 trials to get answers. 2. the second one uses the quadratic formula that students can find in any algebra book. This formula must be used for all quadratic equations that can not be factored.

You simplify the brackets first and then you will have linear equations without brackets!

Without an equality sign and no square variable the given terms can not be that of a quadratic equation.