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

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Answer 1 · 2018-06-18T12:15:20

See a solution process below:

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

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

Therefore their product in standard form would be:

$x (x + 2) = 624$ $x(x + 2) = 624$

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

$x^{2} + 2 x - 624 = 624 - 624$ $x^2 + 2x - color(red)(624) = 624 - color(red)(624)$

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

We can factor this as:

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

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

Solution 1:

$x + 26 = 0$ $x + 26 = 0$

$x + 26 - 26 = 0 - 26$ $x + 26 - color(red)(26) = 0 - color(red)(26)$

$x + 0 = - 26$ $x + 0 = -26$

$x = - 26$ $x = -26$

Solution 2:

$x - 24 = 0$ $x - 24 = 0$

$x - 24 + 24 = 0 + 24$ $x - 24 + color(red)(24) = 0 + color(red)(24)$

$x - 0 = 24$ $x - 0 = 24$

$x = 24$ $x = 24$

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

$- 26 + 2 = - 24$ $-26 + 2 = -24$

$- 26 \cdot - 24 = 624$ $-26 * -24 = 624$

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

$24 + 2 = 26$ $24 + 2 = 26$

$24 \cdot 26 = 624$ $24 * 26 = 624$

There are two solutions to this problem:

${- 26, - 24}$ ${-26, -24}$ ; ${24, 26}$ ${24, 26}$