Question

Use the table to answer the question.

x Substituted Evaluate True Statement?
−23
−
23

0
12
For the quadratic equation x2+20x=69
𝑥
2
+
20
𝑥
=
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=
𝑥
=
is in the solution set.

Answer 1

To determine which values of \( x \) are solutions to the equation \( x^2 + 20x = 69 \), we will first rewrite the equation in standard form:

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

Next, we will substitute each given \( x \) value into the equation and evaluate it to check if it equals zero.

1. **For \( x = -23 \)**:
\[
(-23)^2 + 20(-23) - 69 = 529 - 460 - 69 = 0
\]
True statement: Yes, \( -23 \) is a solution.

2. **For \( x = 0 \)**:
\[
(0)^2 + 20(0) - 69 = 0 + 0 - 69 = -69
\]
True statement: No, \( 0 \) is not a solution.

3. **For \( x = 12 \)**:
\[
(12)^2 + 20(12) - 69 = 144 + 240 - 69 = 315
\]
True statement: No, \( 12 \) is not a solution.

Now we summarize the results in the table:

| x | Substituted | Evaluate | True Statement? |
|-------|---------------------------|-----------|---------------------------|
| -23 | \((-23)^2 + 20(-23) - 69\) | 0 | Yes |
| 0 | \(0^2 + 20(0) - 69\) | -69 | No |
| 12 | \(12^2 + 20(12) - 69\) | 315 | No |

The only value from the given set that is in the solution set is:

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