Answer
the solution set is\[\left\{ -9,2 \right\}\].
Work Step by Step
Step 1:Shift all nonzero terms to left side and obtain zero on the other side.
For this, subtract 18 from both the sides as follows:
\[{{x}^{2}}+7x-18=18-18\]
This implies that,
\[{{x}^{2}}+7x-18=0\]
So, after shifting all nonzero terms to the left side, the above equation becomes: \[{{x}^{2}}+7x-18=0\]
Step 2:Find the factor of the above equation:
Consider the equation,\[{{x}^{2}}+7x-18=0\]
Factorize it as follows:
\[\begin{align}
& {{x}^{2}}+7x-18=0 \\
& {{x}^{2}}+9x-2x-18=0 \\
& x\left( x+9 \right)-2\left( x+9 \right)=0 \\
& \left( x-2 \right)\left( x+9 \right)=0
\end{align}\]
Steps 3 and 4: Set each factor equal to zero and solve the resulting equation:
From step 2, \[\left( x-2 \right)\left( x+9 \right)=0\].
By the zero product principal, either \[\left( x-2 \right)=0\]or\[\left( x+9 \right)=0\].
Now \[\left( x-2 \right)=0\] implies that\[x=2\] and \[\left( x+9 \right)=0\]implies that\[x=-9\].
Step5: Check the solution in the original equation.
Check for\[x=2\]. So consider,
\[\begin{align}
& {{x}^{2}}+7x-18=0 \\
& {{\left( 2 \right)}^{2}}+7\times 2-18=0 \\
& 4+14-18=0 \\
& 0=0
\end{align}\]
And, check for\[x=-9\].
\[\begin{align}
& {{x}^{2}}+7x-18=0 \\
& {{\left( -9 \right)}^{2}}+7\times \left( -9 \right)-18=0 \\
& 81-63-18=0 \\
& 0=0
\end{align}\]
Hence, the solution set is\[\left\{ -9,2 \right\}\].
