se 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 values are solutions for the quadratic equation \( x^2 + 20x = 69 \), we will rewrite the equation as:

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

Next, we will substitute each of the given values into the equation \( x^2 + 20x - 69 \) to see if the result equals zero.

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

2. For \( x = 0 \): \[ (0)^2 + 20(0) - 69 = 0 + 0 - 69 = -69 \] This is not a true statement.

3. For \( x = 12 \): \[ (12)^2 + 20(12) - 69 = 144 + 240 - 69 = 315 \] This is not a true statement.

From this analysis, we see that:

• For \( x = -23 \), it satisfies the equation.
• For \( x = 0 \) and \( x = 12 \), they do not satisfy the equation.

Thus, the solution set contains only the value \( -23 \).

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