Solve the equation x squared plus 3x minus 18 equals 0 by factoring.

Step-by-step solution

1. 1

   State what the two numbers must do. For $x^2+3x-18$ you need a pair with

   $\text{product}=-18,\qquad\text{sum}=+3$

2. 2

   Read the signs first. The product is negative, so the numbers have opposite signs; the sum is positive, so the larger number is the positive one. Among the factor pairs of $18$ — $1\cdot 18$, $2\cdot 9$, $3\cdot 6$ — the pair differing by $3$ is $3$ and $6$.

3. 3

   Assign the signs and factor. Taking $+6$ and $-3$: product $-18$, sum $+3$ $\checkmark$.

   $x^2+3x-18=(x+6)(x-3)$

   Expanding back gives $x^2-3x+6x-18=x^2+3x-18$ $\checkmark$.

4. 4

   Split with the zero product property.

   $(x+6)(x-3)=0\ \Longrightarrow\ x=-6\ \text{or}\ x=3$

5. 5

   Substitute to confirm.

   $(-6)^2+3(-6)-18=36-18-18=0\quad\checkmark$

   $3^2+3(3)-18=9+9-18=0\quad\checkmark$