# How do you use factoring to solve this equation x^2+x=56?

May 23, 2015

${x}^{2} + x = 56$
${x}^{2} + x - 56 = 0$

We can Split the Middle Term of this expression to factorise it.

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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot \left(- 56\right) = - 56$
and
${N}_{1} + {N}_{2} = b = 1$

After trying out a few numbers we get ${N}_{1} = 8$ and ${N}_{2} = - 7$
$8 \cdot \left(- 7\right) = - 56$, and $8 + \left(- 7\right) = 1$

${x}^{2} + x - 56 = {x}^{2} + 8 x - 7 x - 56$
$x \left(x + 8\right) - 7 \left(x + 8\right)$

$\left(x - 7\right) \left(x + 8\right)$ is the factorised form

color (red)(x = 7, x = -8 are the solutions for the expression.