What are the exact solutions of x² = 5x + 2?

Solution:

Given: Equation is x² = 5x + 2

Rearrange the terms as quadratic ax² + bx + c =0

⇒ x² - 5x - 2 = 0

Comparing the coefficients with general equation ax² + bx + c =0, we get

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

x = {-b ± √(b² - 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 x² = 5x + 2?

Summary:

The exact solutions of x² = 5x + 2 are x = {5 ± √33} / 2.