Solve the equation by factoring.

5x^2+9x-72=0

x=__

1 answer

To solve the equation by factoring, we need to find two numbers whose product is -72 and whose sum is 9.

The factors of -72 are (-1, 72), (1, -72), (-2, 36), (2, -36), (-3, 24), (3, -24), (-4, 18), (4, -18), (-6, 12), (6, -12), (-8, 9), and (8, -9).

The pair of numbers that has a sum of 9 is (8, -9).

Therefore, we can rewrite the equation as:

5x^2 + 8x - 9x - 72 = 0.

We can now factor by grouping:

(5x^2 + 8x) + (-9x - 72) = 0.

Factoring out the greatest common factor from the first group and the second group:

x(5x + 8) - 9(5x + 8) = 0.

Now, we can factor out the common binomial (5x + 8):

(5x + 8)(x - 9) = 0.

Setting each factor equal to zero:

5x + 8 = 0 or x - 9 = 0.

Solving each equation:

5x = -8 or x = 9.

Dividing both sides of 5x = -8 by 5:

x = -8/5.

Therefore, the solutions to the equation 5x^2 + 9x - 72 = 0 are x = -8/5 and x = 9.