Question

What are the exact solutions of x^2 = 5x + 2?

Answer 1

Move everybody to one side
minus 5x+2 both sides
x^2-5x-2=0
use quadratic formula where
if you have
ax^2+bx+c=0
x=$\frac{-b+/- \sqrt{b^{2}-4ac} }{2a}$

1x^2-5x-2=0
a=1
b=-5
c=-2

x=$\frac{-(-5)+/- \sqrt{(-5)^{2}-4(1)(-2)} }{2(1)}$
x=$\frac{5+/- \sqrt{25+8} }{2}$
x=$\frac{5+/- \sqrt{33} }{2}$

aprox
x=5.372281323 or -0.3722813233