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

Answer 1

To determine which of the given values is a solution to the quadratic equation \( x^2 + 20x = 69 \), we first need to rearrange the equation into standard form:

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

Next, we will test each of the values in the list (\(-23\), \(0\), and \(12\)) by substituting them into the equation and checking if it equals zero.

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

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

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

Now, summarizing the results, only \( x = -23 \) satisfies the equation \( x^2 + 20x - 69 = 0 \).

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