Jedida solved the quadratic equation x^2−96=4x

Question

by factoring. Her work is shown below. At which step did Jedida first make a mistake, if at all?

x^2−96=4x
Step 1: x^2+4x−96=0
Add 4x
to both sides.
Step 2: (x+12)(x−8)=0
Factor.
Step 3: x+12=0
or x−8=0
Use the Zero Product Property.
x=−12
or x=8
(1 point)
Responses

She did not make any mistakes.
She did not make any mistakes.

Step 1; she added 4x
to both sides instead of subtracting.
Step 1; she added 4 x to both sides instead of subtracting.

Step 3; she did not apply the Zero Product Property correctly.
Step 3; she did not apply the Zero Product Property correctly.

Step 2; she did not factor the left side of the equation correctly.
Step 2; she did not factor the left side of the equation correctly.

Answer 1

Jedida made a mistake in Step 1.

The initial equation is: \[ x^2 - 96 = 4x \]

In Step 1, she wrote: \[ x^2 + 4x - 96 = 0 \]

This is incorrect because she should have subtracted \( 4x \) from both sides to correctly rearrange the equation. The correct transformation should be: \[ x^2 - 4x - 96 = 0 \]

Thus, the correct response is: Step 1; she added 4x to both sides instead of subtracting.