Question

Solve the quadratic equation. Show all of your steps.
x² + 3x – 5= 0

Answer 1

Answer:

$x = \dfrac{-3 \pm \sqrt{29}}{2}$

Step-by-step explanation:

x² + 3x – 5= 0

-5 = -5 * 1 = -1 * 5

-5 + 1 = -4

-1 + 5 = 4

To factor, we need two integers that multiply to -5 and add to 3. There are no such integers, so the trinomial is no factorable. We use the quadratic formula.

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

$x = \dfrac{-3 \pm \sqrt{3^2 - 4(1)(-5)}}{2(1)}$

$x = \dfrac{-3 \pm \sqrt{9 + 20}}{2}$

$x = \dfrac{-3 \pm \sqrt{29}}{2}$