Hyung-eun is solving the quadratic equation x2−4x−12=0 by grouping. Her work is shown below. At which step does Hyung-eun first make an error? x2−4x−12=0 Step1: x2+(−6x)+2x−12=0 Step 2: (x2+(−6x))+(2x−12)=0 Step 3: x(x+(−6))+2(x−6)=0 x(x−6)+2(x−6)=0 Step 4: (x+6)(x−2)=0 Step 5: x+6=0 or x−2=0 x=−6 or x=2 (1 point) Responses Step 2 Step 2 Step 1 Step 1 Step 4 Step 4 Step 3
Hyung-eun first makes an error in Step 3: x(x−6)+2(x−6)=0. The correct step should be x(x−6)+2(x−6)=0.
Hyung-eun first makes an error at Step 3: x(x+(−6))+2(x−6)=0.
To solve the quadratic equation x^2 - 4x - 12 = 0 by grouping, you need to correctly factorize the quadratic expression.
Let's go through the steps:
Step 1: x^2 + (-6x) + 2x − 12 = 0 (There is no error here)
Step 2: (x^2 + (-6x)) + (2x - 12) = 0 (There is no error here)
Step 3: Let's look at this step closely:
x(x + (-6)) + 2(x - 6) = 0
Here, Hyung-eun mistakenly distributes the 2 to both x and -6. It should be:
x(x - 6) + 2(x - 6) = 0
Step 4: (x + 6)(x - 2) = 0 (There is no error here)
Step 5: x + 6 = 0 or x - 2 = 0 (There is no error here)
So, the error occurs at Step 3 where Hyung-eun mistakenly distributes the 2 to both terms instead of just (x - 6).