Use the table to answer the question.

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(s) is/are in the solution set for the quadratic equation \(x^2 + 20x = 69\), we first need to rearrange the equation:

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

Next, we will substitute each value (-23, 0, and 12) into the equation and evaluate to see if the equation holds true (i.e., equals 0).

Testing each value

1. For \(x = -23\): \[ (-23)^2 + 20(-23) - 69 = 529 - 460 - 69 = 0 \] Thus, the statement is true.

2. For \(x = 0\): \[ (0)^2 + 20(0) - 69 = 0 + 0 - 69 = -69 \] Thus, the statement is false.

3. For \(x = 12\): \[ (12)^2 + 20(12) - 69 = 144 + 240 - 69 = 315 \] Thus, the statement is false.

Now, we summarize the evaluations in the table:

| \(x\) | Substituted | Evaluate | True Statement? | |---------|---------------------------|--------------------------|------------------| | -23 | \((-23)^2 + 20(-23) - 69\) | \(0\) | True | | 0 | \(0^2 + 20(0) - 69\) | \(-69\) | False | | 12 | \(12^2 + 20(12) - 69\) | \(315\) | False |

Conclusion

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

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