Question

How do you solve `x^2 + 24x + 90 = 0`?

Answer 1

Complete the square to find:

`x = -12+-3sqrt(6)`

Explanation:

This can be solved by completing the square.

Also use the difference of squares identity:

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

with `a=(x+12)` and `b=3sqrt(6)` as follows:

`0 = x^2+24x+90`

`= (x+12)^2-144+90`

`= (x+12)^2-54`

`= (x+12)^2-(3^2*6)`

`= (x+12)^2-(3sqrt(6))^2`

`= ((x+12)-3sqrt(6))((x+12)+3sqrt(6))`

`= (x+12-3sqrt(6))(x+12+3sqrt(6))`

Hence:

`x = -12+-3sqrt(6)`