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.
Remaining Attempts : 3
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Answer 1

To determine which values from the table are solutions to the quadratic equation \( x^2 + 20x = 69 \), we first need to rearrange the equation to set it to zero:

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

Next, we will substitute each given value of \( x \) into this equation and evaluate it to see if the equation holds true (i.e., equals 0).

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

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

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

After evaluating each value:

- The only value for which the equation \( x^2 + 20x - 69 = 0 \) holds true is \( x = -23 \).

Therefore, the answer is:
**Only \( x = -23 \) is in the solution set.**