Question

The product of two consecutive positive even integers is 14 more than their sum. Set up an equation that can

used to find the two numbers and solve it.

Answer 1

+/- 2 both work.

Explanation:

Remark

To make sure they are even, you need to use 2x and 2x + 2

Equation

2x (2x + 2) = 2x + 2x + 2 + 14 Combine like terms on the right

Solution

2x(2x + 2) = 4x + 16 Remove the brackets

4x^2 + 4x = 4x + 16 Subtract 4x from both sides.

-4x -4x

4x^2 = 16 Divide by 4

x^2 = 16/4

x^2 = 4 Take the square root of both sides

x = +/- 2

Question

Does - 2 work?

2(-2)(-2*2 + 2) = 4(-2)+2 + 14

-4(-4 + 2) = - 8 +2+ 14

-4( - 2) = - 8 + 2+ 14

8 = 8

Yes it does