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 is a solution for the quadratic equation \( x^2 + 20x = 69 \), we first rearrange the equation into standard form:

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

Next, we will substitute each value of \( x \) into the equation and check if the left-hand side equals 0, thereby verifying if it is a solution.

Let's evaluate each of the given values:

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

2. For \( x = 0 \):
\[
(0)^2 + 20(0) - 69 = 0 + 0 - 69 = -69
\]
True statement: No, \( x = 0 \) is not a solution.

3. For \( x = 12 \):
\[
(12)^2 + 20(12) - 69 = 144 + 240 - 69 = 144 + 240 - 69 = 315
\]
True statement: No, \( x = 12 \) is not a solution.

Now compiling our findings, we see that only \( x = -23 \) satisfies the equation.

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