# How do you solve  x^2 + 9x + 8 = 0 by factoring?

Aug 20, 2015

The solutions are
color(blue)( x=-1
color(blue)(x=-8

#### Explanation:

${x}^{2} + 9 x + 8 = 0$

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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot 8 = 8$
and
${N}_{1} + {N}_{2} = b = 9$

After trying out a few numbers we get ${N}_{1} = 8$ and ${N}_{2} = 1$

$8 \cdot 1 = 8$, and $8 + 1 = 9$

${x}^{2} + 9 x + 8 = {x}^{2} + 8 x + 1 x + 8$

$x \left(x + 8\right) + 1 \left(x + 8\right) = 0$

$\textcolor{b l u e}{\left(x + 1\right) \left(x + 8\right)} = 0$ is the factorised form of the equation.

Now we equate the factors to the R.H.S(0)
x+1=0,color(blue)( x=-1
x+8=0, color(blue)(x=-8