# How do you solve x^2 + 5x – 6 = 0?

Aug 20, 2015

The solutions are

color(green)(x=-6

 color(green)(x=1

#### Explanation:

 x^2+5x–6=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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot - 6 = - 6$

and

${N}_{1} + {N}_{2} = b = 5$

After trying out a few numbers we get :

${N}_{1} = - 1$ and ${N}_{2} = 6$

$6 \cdot - 1 = - 6$, and $6 + \left(- 1\right) = 5$

 x^2+5x–6= x^2+6x-1x–6

$x \left(x + 6\right) - 1 \left(x + 6\right) = 0$

$\left(x + 6\right)$ is a common factor to each of the terms

color(green)((x+6)(x-1)=0

We now equate factors to zero:

x+6=0, color(green)(x=-6

x-1=0, color(green)(x=1