# One number is 9 more than another number. If the product of the two numbers is -20, how do you find both numbers?

Jan 10, 2017

One number be $- 5$ and another number be $4$
[or]
One number be $- 4$ and another number be $5$

#### Explanation:

Let the given number be $a$
Then the next number be $b$

$b = a + 9$

Form the equation -

$a \times \left(a + 9\right) = - 20$

Solve it for $a$

${a}^{2} + 9 a = - 20$
${a}^{2} + 9 a + 20 = 0$
${a}^{2} + 5 a + 4 a + 20 = 0$
$a \left(a + 5\right) + 4 \left(a + 5\right) = 0$
$\left(a + 5\right) \left(a + 4\right) = 0$

$a + 5 = 0$
$a = - 5$
$a + 4 = 0$
$a = - 4$

If $a = - 5$

$b = a + 9$
$b = - 5 + 9 = 4$

If $a = - 4$

$b = a + 9$
$b = - 4 + 9 = 5$

One number be $- 5$ and another number be $4$
[or]
One number be $- 4$ and another number be $5$