Question

Question

Jedida solved the quadratic equation x2−96=4x
by factoring. Her work is shown below. At which step did Jedida first make a mistake, if at all?

x2−96=4x

Step 1: x2+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

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

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

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.

She did not make any mistakes.

Answer 1

Jedida's mistake occurred in Step 1. Instead of adding \(4x\) to both sides of the equation, she should have subtracted \(4x\) to move it to the left side.

So, the correct equation after Step 1 should be:

\[ x^2 - 4x - 96 = 0 \]

Since she added \(4x\) instead, her equation was incorrect from that point forward. Therefore, the answer is:

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