Question

The product of two consecutive integers is 72. The equation x(x + 1) = 72 represents the situation, where

represents the smaller integer. Which equation can be factored and solved for the smaller integer?
0 x² + x - 72=0
x² + x + 72 = 0
0x² + 2x - 72=0
0x² + 2x + 72=0

Answer 1

B

Explanation:

2023 sorry about the typo.

Answer 2

x^2 + x - 72 = 0

Explanation:

The equation x(x + 1) = 72, when expanded by doing the indicated multiplication, comes out to x^2 + x - 72 = 0.

That's alll you have to do here.

But if you want to go all the way and find the actual value of x (the smaller integer), factor x^2 + x - 72 = 0 as follows:

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

Setting each factor = to 0 separately, we obtain the solution set {-9, 8}.

If we choose -9 to be the smaller integer, then the next integer is -8. Note that (-9)(-8) = 72.

If we choose 8 to be the smaller integer, then the next integer is 9. Note that (9)(8) = 72.

Note: None of the four possible answers you've shared is correct. The correct quadratic equation does not begin with 0; it begins with 1:

1x^2 + x - 72 = 0