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What is the quadratic formula and what methods can solve the quadratic equation without the formula?
For any quadratic equation a*x^2 + b*x + c = 0, the two solutions are: x = [-b ± sqrt(b^2 - 4*a*c)]/(2*a). The quadratic formula can always be used to generate the solutions to a quadratic equation, but there are other (sometimes simpler and faster) methods.
Factoring can be useful when there are 2 real rational solutions to the equation. Factoring will be easier and faster if you know your multiplication table.
Take for example the following: x^2 + 8*x + 15. What two numbers will multiply to get 15, and add to get 8: Well the factors of 15 are (1 and 15) or (3 and 5), and the 3 and 5 works, so it factors into (x + 3)*(x + 5) = 0. The solutions are x = -3 and x = -5. This works because if the (x+3) factor is zero, then the whole thing equals zero, and x = -3 makes the (x+3) factor equal zero. Same for the (x+5) factor.
Completing the square is another way: Take this one: x^2 + 6*x + 8 = 0. This one is not hard to factor, but use completing the square. A perfect square quadratic (x + a)^2 = x^2 + 2*a*x + a^2, so can we get it into this form. 2*a needs to equal 6, so a = 3 and a^2 = 9, so we have x^2 + 6*x + 9, so how do we get there from our equation: 9 = 8 + 1, so add 1 to both sides:
x^2 + 6*x + 9 = 1. Now we have a perfect square (x + 3)^2 = 1, and take the square root of both sides: x + 3 = ± 1, so x = -4, and x = -2.
Completing the square is actually the method used to come up with the quadratic formula.
What else can I help you with?
What are the steps to solving a quadratic equation?
In general, there are two steps in solving a given quadratic equation in standard form ax^2 + bx + c = 0. If a = 1, the process is much simpler. The first step is making sure that the equation can be factored? How? In general, it is hard to know in advance if a quadratic equation is factorable. I suggest that you use first the new Diagonal Sum Method to solve the equation. It is fast and convenient and can directly give the 2 roots in the form of 2 fractions. without having to factor the equation. If this method fails, then you can conclude that the equation is not factorable, and consequently, the quadratic formula must be used. See book titled:" New methods for solving quadratic equations and inequalities" (Trafford Publishing 2009) The second step is solving the equation by the quadratic formula. This book also introduces a new improved quadratic formula, that is easier to remember by relating the formula to the x-intercepts with the parabola graph of the quadratic function.
What are the solution to the quadratic equation below 12x2 plus 4x-50?
Without an equality sign the given expression can't be considered to be an equation but if it equals 0 then using the quadratic equation formula will give its solutions.
What are the solutions to the equation 2x2 plus 3x-50?
Without an equality sign the given quadratic expression can't be classed as an equation but knowing how to use the quadratic equation formula would be helpful when given such problems.
Can you solve a quadratic equation without factoring?
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)
What is thedifrent betweena quadratic equation and a quadratic function?
An equation just has an equal sign. A function is basically just an equation without one!
How do I put the quadratic formula into a calculator?
The quadratic formula is x=-b±√b^2-4ac divided by 2a. You can only use this formula to solve the quadratic equation: ax^2+bx+c=0 If you were to punch the quadratic formula in the calculator, you would have to punch in the formula except replace the variables with the numbers from the equation. Ex. x^2+2x+1=0 a=1; b=2; c=1 In the calculator you would punch in x=-2±√2^2-4(1)(1) Or simply the equation without x=
How many existing methods are there in solving quadratic equations?
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.
2x square plus 11x plus 5 equals?
The given expression is a quadratic equation. To find its solutions, we can either factor the equation or use the quadratic formula. However, without an equation to solve or any context, it is not possible to provide a numeric answer.
What is the quadratic equation of 6x 7 -2x in standard form?
Without an equality sign and no square variable the given terms can not be that of a quadratic equation.
What are two algebraic methods for solving quadratic equations?
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.
How do you solve quadratic equations by factoring?
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)
What is the quadratic equation of 4x22 7x?
Without an equality sign it can't be an equation but some kind of algebraic expression
