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What does it mean in algebra to complete the square?
A quadratic equation can be solved by completing the square which gives more information about the properties of the parabola than with the quadratic equation formula.
Is there a solution to the quadratic equation of 3x squared -10x equals -5?
Yes because rearranging it into the form of 3x2-10x+5 = 0 makes the discriminant of the quadratic equation greater than zero which means it will have two different solutions. Solving the equation by means of the quadratic formula gives x as being 2.721 or 0.613 both corrected to 3 decimal places.
How many sides does an irregular polygon have if it has 252 diagonals showing work?
Let its sides be x and rearrange the diagonal formula into a quadratic equation:- So: 0.5(x^2-3x) = 252 Then: x^2-3n-504 = 0 Solving the quadratic equation: gives x a positive value of 24 Therefore the polygon has 24 sides irrespective of it being irregular or regular
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.
Two numbers have a product of 80 their sum is 24?
Let's denote the two numbers as x and y. We know that xy = 80 and x + y = 24. We can solve this system of equations by substituting one equation into the other. By substituting y = 24 - x into the first equation, we get x(24 - x) = 80. Simplifying this equation gives us a quadratic equation: x^2 - 24x + 80 = 0. Solving this quadratic equation will give us the values of x and y.
What does it mean in algebra to complete the square?
A quadratic equation can be solved by completing the square which gives more information about the properties of the parabola than with the quadratic equation formula.
When using the quadratic formula x always has multiple correct solutions?
Not necessarily. Formula gives two values but they can be identical.
How do you solve S squared plus 4s minus 21 equals to 0?
To solve the quadratic equation, S^2 + 4S - 21 = 0, you can factor the expression or use the quadratic formula. Factoring, we can rewrite it as (S-3)(S+7) = 0. This means that either S-3 = 0 or S+7 = 0. Solving for S in each case gives S = 3 or S = -7 as the solutions to the equation.
Is there a solution to the quadratic equation of 3x squared -10x equals -5?
Yes because rearranging it into the form of 3x2-10x+5 = 0 makes the discriminant of the quadratic equation greater than zero which means it will have two different solutions. Solving the equation by means of the quadratic formula gives x as being 2.721 or 0.613 both corrected to 3 decimal places.
What are the solutions to x squared minus twelve x plus sixteen equals zero?
Quadratic formula gives roots as 1.53 and 10.47 (to nearest hundredth.)
Simplify 2t squared plus 8t plus 5 equals 0?
Let's simplify this together, friend. To solve the equation 2t^2 + 8t + 5 = 0, we can use the quadratic formula or factor it. If we factor, we look for two numbers that multiply to 2*5=10 and add up to 8. Once we find those numbers, we can rewrite the equation in factored form to find the solutions for t. Just take your time and enjoy the process of unraveling this mathematical mystery.
What is the third step in solving this equation by completing the square?
Completing the square is one method for solving a quadratic equation. A quadratic equation can also be solved by several methods including factoring, graphing, using the square roots or the quadratic formula. Completing the square will always work when solving quadratic equations and is a good tool to have. Solving a quadratic equation by completing the square is used in a lot of word problems.I want you to follow the related link that explains the concept of completing the square clearly and gives some examples. that video is from brightstorm.
What are some examples of how to use the quadratic formula?
For a quadratic equation in the form: ax² + bx + c = 0 The quadratic formula comes from completing the square of the quadratic equation that gives you a result of x=-b±√b²-4ac divided by 2a. Using a simple quadratic equation like x² + 2x + 1 = 0 a=1; b=2; c=1 x=-2±√2²-4(1)(1) divided by 2a x=-2±√4-4 divided by 2a (4 - 4 = 0 and the square root of 0 is 0) Therefore, x=-2
What is -16t2 plus 70t - 65?
There are no integer roots of this equation. Using the quadratic formula gives roots of 1.34 and 3.04 plus or minus loose change in each case.
How are the sum and product of the solutions of a quadratic equation related to the coefficients of the equation?
If you have a quadratic, which is factored like (x - P)(x - Q) = 0, so P & Q are solutions for x. Multiplying the binomials gives: x2 - Px - Qx + PQ = 0 ---> x2 - (P+Q)x + PQ = 0, so the negative of the sum is the coefficient of the x term, and the product is the constant term (no variable x).
How do you solve complex cases of quadratic equations?
If the discriminant - the part under the radical sign in the quadratic formula - is negative, then the result is complex, it is as simple as that. You can't convert a complex number to a real number. If a particular problem requires only real-number solutions, then - if the formula gives complex numbers - you can state that there is no solution.
What is the quadratic equation with the solutions -1 an 5?
The equation must have roots of x = -1 and x = 5 So: x + 1 = 0 and x - 5 = 0 Therefore: (x + 1)(x - 5) = 0 Expanding the brackets gives the equation: x2 - 4x - 5 = 0
