What is the positive solution to this equation?

Question

4x^2 + 12x = 135

Please explain how to.

Answer 1

Hi Lia W.

4x² + 12x = 135

First Subtract 135 from both sides of the equation to give

4x² + 12x - 135 = 0

This can be factored directly since you need factors of 135 that add or subtract to a middle term of positive 12 when multiplied by factors of 4x²

You can experiment and check this but the factors are 9 and 15 for 135 and 2x and 2x for 4x²

(2x - 9)(2x +15) = 0

Since you only need the positive result

2x - 9 = 0

Add 9 to both sides of the equation

2x = 9

Divide both sides by 2

x = 4.5

The other factor gives a negative result so you need not evaluate that one

By the way since this is not so easily factored, you can check it using the Quadratic Formula give that a try

Hope this helps

Answer 2

Answer 3

4x² + 12x - 135 = 0

4(-135) = -540

What two factors of -540 have a sum of 12?

-54 + 10 = -44. Nope

30 + (-18) = 12. Ding, ding, ding, ding!

4x² + 30x - 18x - 135 = 0

2x(2x + 15) - 9x(2x + 15) = 0

(2x - 9)(2x + 15) = 0

2x - 9 = 0

2x = 9

x = 9/2

2x + 15 = 0

2x = -15

x = -15/2

So, our answer is 9/2, aka 4 1/2 or 4.5.