# How do you solve 2x^2 + x - 1=0 by factoring?

Aug 17, 2015

The solutions are
color(blue)(x=-1,x=1/2

#### Explanation:

2x^2+x−1=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:

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

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

2x^2+x−1=2x^2+2x-1x−1

$2 x \left(x + 1\right) - 1 \left(x + 1\right) = 0$

$\left(2 x - 1\right) \left(x + 1\right) = 0$
Now we equate the factors to zero
2x-1=0, color(blue)(x=1/2
x+1=0, color(blue)(x=-1