Algebra Homework Help
Eloise started to solve a radical equation in this way: − 3 = x − 3 + 3 = x + 3 = x + 3 − 1 = x + 3 − 1 = x + 2 ( )2 = (x − 4)2 −2x = x2 − 8x + 16 −2x + 2x = x2 + 8x + 16 + 2x 0 = x2 + 10x + 16
Eloise started to solve a radical equation in this way:
− 3 = x − 3 + 3 = x + 3 = x + 3− 1 = x + 3 − 1 = x + 2 ( )2 = (x − 4)2−2x = x2 − 8x + 16−2x + 2x = x2 + 8x + 16 + 2x 0 = x2 + 10x + 160 = (x + 2)(x + 8)
x + 2 = 0 x + 8 = 0x + 2 − 2 = 0 − 2 x + 8 − 8 = 0 − 8 x = −2 x = −8
Both solutions are extraneous because they don’t satisfy the original equation.
What error did Eloise make? (2 points)
a
She added 2x after squaring both sides.
b
She subtracted 1 before squaring both sides.
c
She factored x2 + 10x + 16 incorrectly.
d
She did not check for extraneous solutions.