Question

What are the solutions to the equation x^2-8x=24

Answer 1

`x^(2) - 8x = 24`

Transposing the equation to give zero on the RHS:

`x^(2) - 8x - 24 = 0`

Since we can't factorise it directly, we must complete the square to yield any solutions:

`x^(2) - 8x + ( (8)/(2))^2 - ((8)/(2))^2 - 24 = 0`

`(x^(2) - 8x + 16) - 16 - 24 = 0`

`(x-4)^2 - 40 = 0`

`(x-4)^2 = 40`

`x-4 = +/- √(40)` ––> because square rooting yields a positive and negative solution.
x = 4 +/-
`√(40)`
x = 4 +/-
`2 √(10)`

Correct me if I'm wrong anyone.