Question

Solve.

x^2+5x−2=0

Enter your answers as exact values.

Answer 1

The polynomial is not factorable, so we use the quadratic formula.

x^2 + 5x − 2 = 0

$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

$x = \dfrac{-5 \pm \sqrt{5^2 - 4(1)(-2)}}{2(1)}$

$x = \dfrac{-5 \pm \sqrt{25 + 8}}{2}$

$x = \dfrac{-5 \pm \sqrt{33}}{2}$

$x = \dfrac{-5 + \sqrt{33}}{2}~~or~~x = \dfrac{-5 - \sqrt{33}}{2}$

$x = -\dfrac{5}{2} + \dfrac{\sqrt{33}}{2}~~or~~x = -\dfrac{5}{2} - \dfrac{\sqrt{33}}{2}$