# Question #6b965

Dec 7, 2017

The two numbers are either -36 and -15
Or they are 15 and 36.

#### Explanation:

Let the smaller number be $x$ and let the larger number be $y$.

By putting the words into equations, we get
$x y = 540$
and
$y = x + 21$

Use substitution to substitute the second equation into the first:
$x \left(x + 21\right) = 540$

${x}^{2} + 21 x - 540 = 0$

Use the quadratic formula:
$x = \frac{- 21 \pm \sqrt{{21}^{2} - 4 \left(- 540\right)}}{2}$

$x = \frac{- 21 \pm 51}{2}$

$x = - 36 , 15$

$y = - 15 , 36$