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Use the table to answer the question.

x Substituted Evaluate True Statement?
−23
0
12
For the quadratic equation x^2+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.

1 answer

To determine which of the values \( x = -23, 0, \) and \( 12 \) are solutions to the equation \( x^2 + 20x = 69 \), we will first rewrite the equation in standard form:

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

Next, we will substitute each value of \( x \) into the left side of the equation \( x^2 + 20x \) and check if it equals 69.

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

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

  3. For \( x = 12 \): \[ (12)^2 + 20(12) = 144 + 240 = 384 \] False

Now, let's fill in the table:

\[ \begin{array}{|c|c|c|c|} \hline x & \text{Substituted} & \text{Evaluate} & \text{True Statement?} \ \hline -23 & (-23)^2 + 20(-23) & 69 & \text{True} \ 0 & 0^2 + 20(0) & 0 & \text{False} \ 12 & 12^2 + 20(12) & 384 & \text{False} \ \hline \end{array} \]

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