Question

Solve this system : y(y-36)=-66

Answer 1

First, distribute the y into the parentheses;
$y(y-36)=-66\\y^{2}-36=-66$
Set all equal to 0;
$y^{2}-36y=-66\\y^{2}-36y+66=0$
That can't be factored normally, so use the quadratic formula;
$\frac{-b(+-)\sqrt{b^{2}-4ac}}{2a}\\\\ \frac{-(-36)(+-)\sqrt{(-36)^{2}-4(1)(66)}}{2*1}\\\\ \frac{36(+-)\sqrt{1296-264)}}{2}\\\\ \frac{18(+-)\sqrt{1034}}{1}\\\\ 18(+-)\sqrt{1034}$
The square root of 1034 cannot be simplified, so the solution(s) are:
$y = 18+\sqrt{1034}=50.155870...$
and
$y=18-\sqrt{1034} = -14.155870...$