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=
`(5+/- √(25+8) )/(2)`
x=
`(5+/- √(33) )/(2)`

aprox
x=5.372281323 or -0.3722813233