# The product of two consecutive even integers is 624. How do you find the integers?

Jun 18, 2018

See a solution process below:

#### Explanation:

First, let's call the first number: $x$

Then the next consecutive even integer would be: $x + 2$

Therefore their product in standard form would be:

$x \left(x + 2\right) = 624$

${x}^{2} + 2 x = 624$

${x}^{2} + 2 x - \textcolor{red}{624} = 624 - \textcolor{red}{624}$

${x}^{2} + 2 x - 624 = 0$

We can factor this as:

(x + 26)(x - 24) = 0

Now, we can solve each term on the left side of the equation for $0$:

Solution 1:

$x + 26 = 0$

$x + 26 - \textcolor{red}{26} = 0 - \textcolor{red}{26}$

$x + 0 = - 26$

$x = - 26$

Solution 2:

$x - 24 = 0$

$x - 24 + \textcolor{red}{24} = 0 + \textcolor{red}{24}$

$x - 0 = 24$

$x = 24$

If the first number is $- 26$ then the second number is:

$- 26 + 2 = - 24$

$- 26 \cdot - 24 = 624$

If the first number is 24 then the second number is:

$24 + 2 = 26$

$24 \cdot 26 = 624$

There are two solutions to this problem:

$\left\{- 26 , - 24\right\}$; $\left\{24 , 26\right\}$