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

Aug 16, 2015

The solutions are:

color(blue)(x=1
color(blue)(x=-7

#### Explanation:

${x}^{2} + 6 x + 2 = 9$
${x}^{2} + 6 x + 2 - 9 = 0$
${x}^{2} + 6 x - 7 = 0$

We can Split the Middle Term of this expression to factorise it and then we 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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot - 7 = - 7$
and
${N}_{1} + {N}_{2} = b = 6$

After trying out a few numbers we get ${N}_{1} = 7$ and ${N}_{2} = - 1$
$7 \cdot \left(- 1\right) = - 7$, and $7 + \left(- 1\right) = 6$

${x}^{2} + 6 x - 7 = {x}^{2} + 7 x - 1 x - 7$
x(x+7)(-1(x+7)=0
$\left(x - 1\right) \left(x + 7\right) = 0$
Now we equate the factors to zero and find the solutions.

x-1=0,color(blue)(x=1
x+7=0,color(blue)(x=-7