Question

Square root of negative 2x plus 1 − 3 = x
Square root of negative 2x plus 1 − 3 + 3 = x + 3
Square root of negative 2x plus 1 = x + 3
Square root of negative 2x plus 1 − 1 = x + 3 − 1
Square root of negative 2 x = x + 2
(Square root of negative 2 x)2 = (x − 4)2
−2x = x2 − 8x + 16
−2x + 2x = x2 + 8x + 16 + 2x
0 = x2 + 10x + 16
0 = (x + 2)(x + 8)

x + 2 = 0 x + 8 = 0
x + 2 − 2 = 0 − 2 x + 8 − 8 = 0

Answer 1

Both solutions are extraneous because they don't satisfy the original equation.

What error did Eloise make?

She added 2x after squaring both sides.

She subtracted 1 before squaring both sides.

She factored x2 + 10x + 16 incorrectly.

She did not check for extraneous solutions.

Answer 2

First you square both sides, then you subtract,
-B
She subtracted 1 before squaring both sides.