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

**Solution:**

Given: Equation is x^{2} = 5x + 2

Rearrange the terms as quadratic ax^{2} + bx + c =0

⇒ x^{2} - 5x - 2 = 0

Comparing the coefficients with general equation ax^{2} + bx + c =0, we get

a = 1, b = -5, c = -2

x = {-b ± √(b^{2} - 4ac)} / 2a

x = {-(-5) ± √((-5)^{2} -4(-2))} / 2(1)

x = {5 ± √(25 +8) }/ 2

x = {5 ± √33} / 2

The solutions of the given equation are x = {5 ± √33} / 2.

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

**Summary:**

The exact solutions of x^{2} = 5x + 2 are x = {5 ± √33} / 2.