# How do you solve x^2 +3x - 18 = 0 by factoring?

Sep 29, 2015

The solutions are

 color(blue)(x=3

 color(blue)(x=-6

#### Explanation:

${x}^{2} + 3 x - 18$

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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot - 18 = - 18$

AND

${N}_{1} + {N}_{2} = b = 3$

After trying out a few numbers we get ${N}_{1} = 6$ and ${N}_{2} = - 3$

$6 \cdot - 3 = - 18$, and $6 + \left(- 3\right) =$

${x}^{2} + 3 x - 18 = {x}^{2} + 6 x - 3 x - 18$

$x \left(x + 6\right) - 3 \left(x + 6\right) = 0$

$\left(x - 3\right) \left(x + 6\right) = 0$

Now we equate the factors to zero to obtain the solutions:

x-3 = 0, color(blue)(x=3

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