Question

What are the solutions of x2 + 5x − 24 = 0? Show all work for full credit.

Answer 1

Factoring! An important mathematical skill.

x^2 + 5x - 24 = 0

Set up your two parentheses:
(x _ _) (x _ _) = 0

We need numbers that sum to +5 and multiply together to -24. This requires us to know the factors of 24: (1,24),(2,12),(3,8),(4,6).

Now, you'll notice that (3,8) has a difference of 5 (8 - 3 = 5), so let's use those!

(x _ 3) (x _ 8) = 0

Now, we need this to produce x-terms which sum to +5, so 8 must be positive, and the 3 negative.

(x - 3) (x + 8) = 0

Now, we simply set each term equal to 0 separately:

x-3 = 0 --> x = 3
x+8 = 0 --> x = -8