# How do you solve x^2+ 15x= -36 by factoring?

Aug 23, 2015

The solutions are
color(blue)(x=-3
 color(blue)(x=-12

#### Explanation:

x^2+15x=−36
${x}^{2} + 15 x + 36 = 0$

We can Split the Middle Term of this expression to factorise it and thereby find solutions.

In this technique, if we have to factorise an expression like $a {x}^{2} + b x + c$, we need to think of 2 numbers such that:

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot 36 = 36$
AND
${N}_{1} + {N}_{2} = b = 15$
After trying out a few numbers we get ${N}_{1} = 12$ and ${N}_{2} = 3$
$12 \cdot 3 = 36$, and $12 + 3 = 15$

${x}^{2} + 15 x + 36 = {x}^{2} + 12 x + 3 x + 36$

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

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

Now we equate the factors to zero

x+3=0, color(blue)(x=-3
x+12=0, color(blue)(x=-12