Eloise started to solve a radical equation in this way: 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 − 8 x = −2 x = −8 both solutions are extraneous because they don't satisfy the original equation. what error did eloise make?

Here I copy the steps and indicate where the error is.

Square root of negative 2x plus 1 − 3 = x=> this is the starting equation

√[ - 2x + 1] - 3 = x

Square root of negative 2x plus 1 − 3 + 3 = x + 3 in this step she added 3 to each side, which is fine

 Square root of negative 2x plus 1 = x + 3 she made the addtions => fine

Square root of negative 2x plus 1 − 1 = x + 3 – 1 due to plus 1 in inside the square root, this step will not help

 Square root of negative 2 x = x + 2 wrong! she cannot simplify - 1 that is out of the square root with +1 that is inside the square root

Then, from here on all is wrong, but she made other additional mistakes.

(Square root of negative 2 x)2 = (x − 4)2 −2x  the right side should be (x+2)^2 which is x^2 + 4x +4 not (x-4)^2 - 2x

Later she made a mistake changing the sign of -8x to +8x

Those are the mistakes. Finally, the global error is that she should verify whether the found values satisfied the original equation.

Iwould say rat and vsu but i’m not 100% sure

820,000 is the answr