# How do you factor x^2 - x = 72?

May 4, 2016

color(green)(( x+8) ( x - 9)  is the factorised form of the expression.

#### Explanation:

${x}^{2} - x = 72$

${x}^{2} - x - 72 = 0$

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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot \left(- 72\right) = - 72$

AND

${N}_{1} + {N}_{2} = b = - 1$

After trying out a few numbers we get ${N}_{1} = - 9$ and ${N}_{2} = 8$
$8 \cdot \left(- 9\right) = - 72$, and $8 + \left(- 9\right) = - 1$

${x}^{2} - x - 72 = {x}^{2} - 9 x + 8 x - 72$

$= x \left(x - 9\right) + 8 \left(x - 9\right)$

= color(green)(( x+8) ( x - 9)