Question

Solve the quadratic equation by factoring. x2+3x−18=0 Enter the exact answers.

Answer 1

The question is given below as

`x^2+3x-18=0`

Step 1:We will look for two factors we will multiply together to get -18 and the same two factors that will add up together to +3

`\begin{gathered} The\text{ factors of 18 are} \\ 1,-1,2,-2,3,-3,6,-6,-9,9,18,-18 \end{gathered}`

Since -18 is a negative value

Then, the two factors must have different signs because of the sign pattern below

`\begin{gathered} -*-=+ \\ +*-=- \\ +*+=+ \end{gathered}`

The two factors are

`\begin{gathered} +6,-3 \\ +6*-3=-18 \\ +6-3=+3 \end{gathered}`

Step 2: Substitute the factors in the equation below

`\begin{gathered} x^2+3x-18=0 \\ x^2+6x-3x-18=0 \\ x(x+6)-3(x+6)=0 \\ (x-3)(x+6)=0 \end{gathered}`

Step 3: Equate both factors to zero

`\begin{gathered} (x-3)=0,(x+6)=0 \\ x=0+3,x=0-6 \\ x=3,x=-6 \end{gathered}`

Hence,

The final answer are x =3 and x = -6