Trey, Amelia, and Cho are discussing the solution set to the equation x^2 +9=45.

Trey says the solution is {6}. Amelia says the solution is {-6,6}. Cho says the solution is {-6}. Which person has found the correct solution set?

1 answer

To solve the equation \( x^2 + 9 = 45 \), we first isolate \( x^2 \):

\[ x^2 + 9 = 45 \]

Subtract 9 from both sides:

\[ x^2 = 45 - 9 \] \[ x^2 = 36 \]

Next, we take the square root of both sides. Remember that when we take the square root, we consider both the positive and negative roots:

\[ x = \pm \sqrt{36} \] \[ x = \pm 6 \]

This gives us the solutions \( x = 6 \) and \( x = -6 \). Therefore, the solution set is:

\[ {-6, 6} \]

Now let's compare the responses:

  • Trey says the solution is \( {6} \) (not correct, as it misses the negative solution).
  • Amelia says the solution is \( {-6, 6} \) (correct).
  • Cho says the solution is \( {-6} \) (not correct, as it misses the positive solution).

The person who has found the correct solution set is Amelia.