Use the table to answer the question.

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 whether the given values (−23, 0, and 12) are solutions to the quadratic equation \( x^2 + 20x = 69 \), we'll substitute each value into the equation and see if the equation holds true.

First, we rearrange the equation to standard form: \[ x^2 + 20x - 69 = 0 \]

Next, we'll substitute each value of \( x \) into the equation \( x^2 + 20x - 69 \) and evaluate.

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

   • True Statement? Yes

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

   • True Statement? No

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

   • True Statement? No

Now, we can complete the table as follows:

| x | Substituted | Evaluate | True Statement? | |-----|---------------------------------|----------|------------------| | -23 | \((-23)^2 + 20(-23) - 69\) | 0 | Yes | | 0 | \(0^2 + 20(0) - 69\) | -69 | No | | 12 | \(12^2 + 20(12) - 69\) | 315 | No |

Conclusion

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