# How do you solve x^2-2x=8?

Sep 12, 2015

color(blue)(x=-2
 color(blue)(x=4

#### Explanation:

x^2−2x- 8 = 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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot - 8 = - 8$
AND
${N}_{1} + {N}_{2} = b = - 2$

After trying out a few numbers we get ${N}_{1} = - 4$ and ${N}_{2} = 2$
$2 \cdot \left(- 4\right) = - 8$ and $2 + \left(- 4\right) = - 2$

x^2−2x- 8 = x^2 color(blue)(- 4x + 2x)- 8

$= x \left(x - 4\right) + 2 \left(x - 4\right)$

color(blue)((x+2) ( x-4) is the factorised form for the expression, we now equate the factors to zero and obtain the solutions.

x+2 = 0, color(blue)(x=-2
x-4 = 0, color(blue)(x=4