Question

Solution Sets of Quadratic Equations Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
2 of 52 of 5 Items







Question
Use the table to answer the question.

x Substituted Evaluate True Statement?
−23

0
12
For the quadratic equation x2+20x=69
, complete the table by testing each of the given values to determine whether it is a solution. Identify which one of these values is in the solution set.

(1 point)
Only x=
is in the solution set.

Answer 1

To determine which value is in the solution set for the quadratic equation \( x^2 + 20x = 69 \), we will first set the equation to equal zero by rearranging it:

\[
x^2 + 20x - 69 = 0
\]

Next, we'll evaluate the equation for each of the given \( x \) values in the table: \( -23 \), \( 0 \), and \( 12 \).

1. **For \( x = -23 \)**:
\[
(-23)^2 + 20(-23) - 69 = 529 - 460 - 69 = 0
\]
**True Statement? Yes, it equals 0.**

2. **For \( x = 0 \)**:
\[
(0)^2 + 20(0) - 69 = 0 + 0 - 69 = -69
\]
**True Statement? No, it does not equal 0.**

3. **For \( x = 12 \)**:
\[
(12)^2 + 20(12) - 69 = 144 + 240 - 69 = 315
\]
**True Statement? No, it does not equal 0.**

After evaluating all the values, we conclude:

- \( -23 \) is in the solution set since it satisfies the equation \( x^2 + 20x - 69 = 0 \).
- The values \( 0 \) and \( 12 \) do not satisfy the equation.

Therefore:

**Only \( x = -23 \) is in the solution set.**