Question

The product of two consecutive positive even integers is 12,320. What are the two integers?

Answer 1

We can use an equation where the first number is

x

and the second number is

x+2

so we have

x(x+2) = 12320

then multilply on the left-side

x^2 + 2x = 12320

and subtract 12320 on both sides

x^2 + 2x - 12320 = 0

Do you know the next step?

Answer 2

divide both sides by 2?

Answer 3

Not quite ... factor .....

x^2 + 2x - 12320 = (x + 112)(x - 110)

So we have

(x + 112)(x - 110) = 0

Do you know the next step?

Answer 4

combine like terms?

Answer 5

solve each factor

x + 112 = 0

or

x = -112

but this is not positive

x - 110 = 0

or

x =110

The answers are 110 and 112

Answer 6

Great! thank you so much for explaining your steps!