The product of two consecutive integers is 72. F ind all solutions.

x = - 9 0r - 8

x = 8 0r 9

Step-by-step explanation:

let the two consecutive integers be

x

and x + 1

so, the product of the two integers that is equal to 72 will be

x (x + 1) = 72

x² + x = 72

x² + x - 72 = 0

note this expression x² + x - 72 = 0 also looks like a quadratic equation

ax² + bx + c = 0

using the quadratic formula

x = - b±√b² - 4ac/2a

where b a = 1

b = 1

c = - 72

x = - b± √ 1² - 4 (1) * (-72) / 2 (1)

x = - 1 ± √ 1 + 288/2

x = - 1± √289/2

x = - 1 ± 17/2

x = - 1-17/2 or - 1 + 17/2

x = - 18/2 0r 16/2

x = - 9 or x = 8

so we have four answers that satisfy the initial equation

from

either

x = - 9 or (x + 1) = - 9 + 1 = - 8

-9 x - 8

72

also x = 8

0r (x + 1) = 8+1 = 9

that is, 8 x 9 = 72

Case1: 8,9

Case 2 - 9,-8

Step-by-step explanation:

Let x = 1st integer

(x+1) = consecutive integer

x (x+1) = 72

Distribute

x^2 + x = 72

Subtract 72 from each side

x^2 + x - 72 = 0

Factor

What numbers multiply to - 72 and add to 1

-8 * 9 = - 72

-8+9 = 1

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

Using the zero product property

x-8 = 0 x+9=0

x = 8 x = - 9

Case 1

x=8

x+1 = 9

Case2

x = - 9

x+1 = - 8