# How do you find the solution to the quadratic equation v^2 + 2v - 8 = 0?

May 2, 2015

${v}^{2} + 2 v - 8 = 0$

To solve for v, we need to factorise the expression on the left

We can split the middle term of this expression to factorise it

In this technique, if we have to factorise an expression like $a {v}^{2} + b v + c$, 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 ${N}_{2} = - 2$

$4 \cdot - 2 = 60$, and $4 + \left(- 2\right) = 2$

We write the equation as:
${v}^{2} + 4 v - 2 v - 8 = 0$

$v \left(v + 4\right) - 2 \left(v + 4\right) = 0$

$v + 4$ is a common factor to each of the terms

$\left(v + 4\right) \left(v - 2\right) = 0$

This tells us that:

Either $\left(v + 4\right) = 0$ or $\left(v - 2\right) = 0$

color(green)( v = -4 or v = 2 is the Solution