[tex] x^{2} - 8x = 24[/tex]
Transposing the equation to give zero on the RHS:
[tex] x^{2} - 8x - 24 = 0[/tex]
Since we can't factorise it directly, we must complete the square to yield any solutions:
[tex] x^{2} - 8x + ( \frac{8}{2})^2 - (\frac{8}{2})^2 - 24 = 0[/tex]
[tex] (x^{2} - 8x + 16) - 16 - 24 = 0[/tex]
[tex] (x-4)^2 - 40 = 0[/tex]
[tex] (x-4)^2 = 40[/tex]
[tex] x-4 = +/- \sqrt{40} [/tex] ––> because square rooting yields a positive and negative solution.
x = 4 +/- [tex] \sqrt{40} [/tex]
x = 4 +/- [tex]2 \sqrt{10} [/tex]
Correct me if I'm wrong anyone.
