# How do you solve x^2 + 2x - 15 = 0 by factoring?

Aug 16, 2015

The solutions are
 color(blue)(x=3

color(blue)(x=-5

#### Explanation:

 x^2+2x−15=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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot - 15 = - 15$
AND
${N}_{1} + {N}_{2} = b = 2$

After trying out a few numbers we get ${N}_{1} = 5$ and ${N}_{2} = - 3$
$5 \cdot - 3 = - 15$, and $5 + \left(- 3\right) = 2$

 x^2+2x−15=x^2+5x-3x−15

$x \left(x + 5\right) - 3 \left(x + 5\right) = 0$

$\left(x - 3\right) \left(x + 5\right) = 0$

Now we equate the factors to zero to find the solutions:
x-3 =0, color(blue)(x=3

x+5 =0, color(blue)(x=-5