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)

Answer 1

To determine if the values in the table are solutions to the equation \( x^2 + 20x = 69 \), we can rewrite the equation as \( x^2 + 20x - 69 = 0 \).

Let's substitute each value of \( x \) into the left-hand side of the equation and see if it equals 69. We'll complete the table accordingly.

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

**2. For \( x = 0 \):**
\[
(0)^2 + 20(0) = 0 + 0 = 0
\]
So, the statement is **False**.

**3. For \( x = 12 \):**
\[
(12)^2 + 20(12) = 144 + 240 = 384
\]
So, the statement is **False**.

Now we can fill in the table:

| x | Substituted | Evaluate | True Statement? |
|------|----------------------------------|----------|------------------|
| -23 | (-23)^2 + 20(-23) | 69 | True |
| 0 | (0)^2 + 20(0) | 0 | False |
| 12 | (12)^2 + 20(12) | 384 | False |

**Conclusion:** The only value in the solution set is \( x = -23 \).