What is the sum of the ﻿
2
2﻿ solutions of the equation ﻿
x
2
−
4
x
−
4
5
=
0
x 
2
 −4x−45=0﻿ ?

To find the sum of the solutions of the quadratic equation \(x^2 - 4x - 45 = 0\), we can use Vieta's formulas. For a quadratic equation of the form \(ax^2 + bx + c = 0\), the sum of the solutions \(x_1\) and \(x_2\) is given by:

\[
x_1 + x_2 = -\frac{b}{a}
\]

In your equation, \(a = 1\), \(b = -4\), and \(c = -45\).

Therefore, the sum of the solutions is:

\[
x_1 + x_2 = -\frac{-4}{1} = 4
\]

So, the sum of the solutions is \(4\).

Would you like more details or have any questions? Here are some related questions:

1. How do you find the product of the solutions for the same equation?
2. What are Vieta's formulas, and how do they apply to quadratic equations?
3. Can you solve the quadratic equation \(x^2 - 4x - 45 = 0\) using the quadratic formula?
4. How do you factor the quadratic equation \(x^2 - 4x - 45 = 0\)?
5. What are the roots of the equation \(x^2 - 4x - 45 = 0\)?

**Tip:** Vieta's formulas provide a quick way to find the sum and product of the roots of a quadratic equation without solving it directly.

Learn how to find the sum of solutions for the quadratic equation x^2 - 4x - 45 = 0 using Vieta's formulas. This problem covers key algebraic concepts, including quadratic equations and Vieta's formulas. Suitable for students in Grades 10-12.

Math Problem Statement

What is the sum of the 2 2 solutions of the equation x 2 − 4 x − 4 5

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