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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page 15 of 16

Answer 1

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

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

Next, we'll substitute each of the given values (-23, 0, and 12) into the equation and evaluate to see if the equation holds true (i.e., equals 0).

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

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

3. **For \( x = 12 \)**:
\[
(12)^2 + 20(12) - 69 = 144 + 240 - 69 = 315
\]
This is not true: \( 315 \neq 0 \).

After evaluating all the options, we find that only \( x = -23 \) is a solution to the equation \( x^2 + 20x - 69 = 0 \).

Thus, the correct answer is:
**Only x = -23 is in the solution set.**