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}\\\\ (36(+-)√(1296-264)))/(2)\\\\ (18(+-)√(1034))/(1)\\\\ 18(+-)√(1034)`
The square root of 1034 cannot be simplified, so the solution(s) are:

`y = 18+√(1034)=50.155870...`
and

`y=18-√(1034) = -14.155870...`