# How do you factor and solve x^2+ 15x= -36?

Jun 7, 2016

$x = - 3$
and
$x = - 12$

#### Explanation:

To solve ${x}^{2} + 15 x = - 36$

We begin by setting the equation equal to zero.
${x}^{2} + 15 x + 36 = \cancel{- 36} \cancel{+ 36}$

${x}^{2} + 15 x + 36 = 0$

Now find the factors of 36
$1 \mathmr{and} 36$
$2 \mathmr{and} 18$
$3 \mathmr{and} 12$
$4 \mathmr{and} 9$
$6 \mathmr{and} 6$

Since the second sign of the trinomial is $+$ we must add the factors to get the middle term 15.
Since the first sign of the trinomial is $+$ we know the factor must both be $+$

So the factors are $3 \mathmr{and} 12$

Now factor the trinomial

$\left(x + 3\right) \left(x + 12\right) = 0$

Set each factor equal to zero and solve.

$x + 3 = 0$

$x \cancel{+ 3} \cancel{- 3} = 0 - 3$

$x = - 3$

and
$x + 12 = 0$

$x \cancel{+ 12} \cancel{- 12} = 0 - 12$

$x = - 12$