Question

This is Colby’s solution for the equation x^2-4x-5=0:

x^2-4x-5=0
x^2-4x=5
x^2-4x+4=5+4
(x+2)^2=9
x-2=9
x=11
x-2=-9
x=-7

Looking at Colby’s wok, explain where his answer is incorrect and how to correct it.

Answer 1

See below

Explanation:

Colby made a mistake in the 4th line of his work, where he reduced the trinomial
`x^2-4x+4` into
`(x+2)^2` instead of reducing it to
`(x-2)^2`. He also did not square root both sides of the equation afterward before he made two seperate equations, leading to incorrect answers.

Continuing on from where Colby made his first mistake, this is how you would correctly solve the rest of the problem:

`(x-2)^2=9\\\\x-2=3\\\\x=5\\\\x-2=-3\\\\x=-1`