Question

How do you solve `x^2+2x-120=0` by completing the square?

Answer 1

`x=10` or `x=-12`

Explanation:

The difference of squares identity can be written:

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

Use this with `a=(x+1)` and `b=11` as follows:

`0 = x^2+2x-120`

`color(white)(0) = x^2+2x+1-121`

`color(white)(0) = (x+1)^2-11^2`

`color(white)(0) = ((x+1)-11)((x+1)+11)`

`color(white)(0) = (x-10)(x+12)`

Hence roots `x=10` and `x=-12`