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)

Answer 1

To determine whether the given values (−23, 0, and 12) are solutions to the quadratic equation \( x^2 + 20x = 69 \), we'll substitute each value into the equation and see if the equation holds true.

First, we rearrange the equation to standard form:
\[
x^2 + 20x - 69 = 0
\]

Next, we'll substitute each value of \( x \) into the equation \( x^2 + 20x - 69 \) and evaluate.

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

2. **For \( x = 0 \)**:
\[
(0)^2 + 20(0) - 69 = 0 + 0 - 69 = -69
\]
- **True Statement?** No

3. **For \( x = 12 \)**:
\[
(12)^2 + 20(12) - 69 = 144 + 240 - 69 = 315
\]
- **True Statement?** No

Now, we can complete the table as follows:

| 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 |

### Conclusion
The only value in the solution set is **\( x = -23 \)**.