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.

Answer 1

To determine whether each value of \( x \) (−23, 0, 12) is a solution to the quadratic equation \( x^2 + 20x = 69 \), we first need to rearrange the equation into standard form:

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

Now we will substitute each value of \( x \) into the equation and check whether the equation holds true.

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

This evaluates to 0, which satisfies the equation \( x^2 + 20x - 69 = 0 \). So, \( x = -23 \) is a solution.

2. **For \( x = 0 \):**
\[
(0)^2 + 20(0) - 69
\]
\[
= 0 + 0 - 69
\]
\[
= -69
\]

This does not evaluate to 0, so \( x = 0 \) is not a solution.

3. **For \( x = 12 \):**
\[
(12)^2 + 20(12) - 69
\]
\[
= 144 + 240 - 69
\]
\[
= 384 - 69
\]
\[
= 315
\]

This does not evaluate to 0, so \( x = 12 \) is not a solution.

Based on the evaluations, we can conclude:

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