Question

How do you solve `x^ { 2} - 2x = 44`?

Answer 1

`x = 1 +-3sqrt(5)`

Explanation:

Complete the square then use the difference of squares identity:

`a^2-b^2 = (a-b)(a+b)`

with `a=(x-1)` and `b=3sqrt(5)` as follows...

Subtract `44` from both sides to get:

`0 = x^2-2x-44`

`color(white)(0) = x^2-2x+1-45`

`color(white)(0) = (x-1)^2-(3sqrt(5))^2`

`color(white)(0) = ((x-1)-3sqrt(5))((x-1)+3sqrt(5))`

`color(white)(0) = (x-1-3sqrt(5))(x-1+3sqrt(5))`

Hence:

`x = 1 +-3sqrt(5)`