Chapter 8, Problem 4STP

To determine

The solution of the given expression.

Answer to Problem 4STP

The correct option is F.

Explanation of Solution

Given:

The expression is given as:

  $x^2+6x-112=0$

The options are given as:

  $\begin{array}{l}F-14H6\\ G-8J12\end{array}$

Rewriting the given expression:

  $\begin{array}{l}{x}^2-8x+14x-112=0\\ \left(x^2-8x\right)+\left(14x-112\right)=0\\ x\left(x-8\right)+14\left(x-8\right)=0\\ \left(x-8\right)\left(x+14\right)=0\end{array}$

Now, solving the above factors:

  $\begin{array}{c}\left(x-8\right)=0\\ x=8\\ \left(x+14\right)=0\\ x=-14\end{array}$

Therefore, the correct option is F.