Question

How do you solve `x²+2x-24=0` algebraically?

Answer 1

Complete the square to find:

`x=4` or `x=-6`

Explanation:

Complete the square `x^2+2x+1` then use the difference of squares identity:

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

with `a=(x+1)` and `b=5` as follows:

`0 = x^2+2x-24`

`=x^2+2x+1-1-24`

`=(x+1)^2-5^2`

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

`=(x-4)(x+6)`

So `x=4` or `x=-6`