\(x^{2} - 8x = 24\)
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.