Ariel is working on her math test. She is trying to solve the equation x^2+4x−12=7

Question

Step 1: Begin with equation. x^2+4x−12=7
Step 2: Write quadratic equation as the product of two factors (x+5)(x−1)=7
Step 3: Set each factor equal to 0. x+5=0 and x−1=0
Step 4: Solve each equation. x=−5 and x=1

choose from these:

on step 2, she should have subtracted 7 from both side before factoring so that the solution is equal to 0.
on step 4, she has her signs wrong, she should not have made them opposites
on step 3, she has her signs wrong. both signs should be positive
on step1, she should have added 4x and -12 together

Answer 1

Ariel made a mistake in Step 2 of her process. The correct approach would be to rearrange the equation so that one side equals zero before factoring. Therefore, she should have subtracted 7 from both sides in Step 1. The correct transformation of the original equation in Step 1 should be:

Step 1: Start with the equation x^2 + 4x - 12 = 7.

Subtract 7 from both sides to get:

x^2 + 4x - 19 = 0.

Then she could factor or use the quadratic formula to solve it correctly. Thus, the correct choice is:

On step 2, she should have subtracted 7 from both sides before factoring so that the solution is equal to 0.