Question

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

Answer 1

`x = (-3 \pm √(29))/(2)`

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 = (-b \pm √(b^2 - 4ac))/(2a)`

`x = (-3 \pm √(3^2 - 4(1)(-5)))/(2(1))`

`x = (-3 \pm √(9 + 20))/(2)`

`x = (-3 \pm √(29))/(2)`