How do you solve 36x = —4x^2 — 50?

1 Answer
Apr 6, 2018

The set of solutions is \{\frac{\sqrt{31}-9}{2}, \frac{-9-\sqrt{31}}{2}\}.

Explanation:

36x=-4x^2-50

\implies 4x^2+36x+50=0

Applying the quadratic formula, which states that if ax^2+bx+c=0, then:

x=\frac{-b\pm\sqrt{\Delta}}{2a}

Where \Delta=b^2-4ac. Solving the equation with our values:

x_{12}=\frac{-36\pm\sqrt{36^2-4\cdot 4\cdot 50}}{8}

x_{12}=\frac{-36\pm 4\sqrt{31}}{8}

x_{12}=\frac{-9\pm \sqrt{31}}{2}

And so the two solutions are \frac{\sqrt{31}-9}{2} and \frac{-9-\sqrt{31}}{2}.