# How do you solve x^2+6x=-9 by factoring?

Aug 16, 2015

The solutions is color(blue)(x=-3

#### Explanation:

${x}^{2} + 6 x + 9 = 0$

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

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot 9 = 9$
AND
${N}_{1} + {N}_{2} = b = 6$
After trying out a few numbers we get ${N}_{1} = 3$ and ${N}_{2} = 3$
$3 \cdot 3 = 9$ and $3 + 3 = 6$

${x}^{2} + 6 x + 9 = {x}^{2} + 3 x + 3 x + 9$

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

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

Now we equate the factors to zero and find the solutions.
x+3 =0, color(blue)(x=-3

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