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:
$x^{2} - 8x + ( \frac{8}{2})^2 - (\frac{8}{2})^2 - 24 = 0$
$(x^{2} - 8x + 16) - 16 - 24 = 0$
$(x-4)^2 - 40 = 0$
$(x-4)^2 = 40$
$x-4 = +/- \sqrt{40}$ ––> because square rooting yields a positive and negative solution.
x = 4 +/- $\sqrt{40}$
x = 4 +/- $2 \sqrt{10}$

Correct me if I'm wrong anyone.