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 which value(s) from the table are solutions to the equation \(x^2 + 20x = 69\), we can rearrange the equation to standard form:

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

Now we will evaluate whether each of the given values (-23, 0, 12) is a solution by substituting them into the equation to see if the left side equals 0.

1. **For \(x = -23\)**:
\[
(-23)^2 + 20(-23) - 69 = 529 - 460 - 69 = 0
\]
This simplifies to:
\[
0 = 0
\]
So, \(x = -23\) is a solution.

2. **For \(x = 0\)**:
\[
(0)^2 + 20(0) - 69 = 0 + 0 - 69 = -69
\]
This simplifies to:
\[
-69 \neq 0
\]
So, \(x = 0\) is not a solution.

3. **For \(x = 12\)**:
\[
(12)^2 + 20(12) - 69 = 144 + 240 - 69 = 315
\]
This simplifies to:
\[
315 \neq 0
\]
So, \(x = 12\) is not a solution.

Thus, the only value from the given list that is in the solution set is:

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