Question

Which of the following is a solution to $x^2+\mathbf{6}x-\mathbf{112}=\mathbf{0}$?

F$-\mathbf{14}$

G$-\mathbf{6}$

H 6

J 12

Short answer

The solution of $x^2+6x-112=0$is $x=-\mathbf{14}\mathbf{,}\mathbf{8}$. Hence the answer is option F.

Step-by-step solution

Step 1. Factor by using GCF.

Factor by using GCF to get the form $xy=0$.

$\left(x+14\right)\left(x-8\right)=0$

Step 2. Write zero product property.

For any real numbers x and y, if$xy=0$ then$x=0,y=0$ or both x and y equal to zero.

Step 3. Apply zero product property.

Apply zero product property to the equation, $\left(x+14\right)\left(x-8\right)=0$.

$$\begin{gathered} x+14=0\text{or}x-8=0 \\ x=-14x=8 \end{gathered}$$

Therefore, the roots are$-14$ and 8.

Step 4. Check the obtained solution.

To check whether the obtained solution is correct or not, substitute $-14$ for x and 8 for x in the given equation and simplify.

role="math" localid="1647693760070" $$\begin{gathered} {\left(-14\right)}^2+6\left(-14\right)-112\stackrel{?}{=}0 \\ 0=0✓ \end{gathered}$$

$$\begin{gathered} {\left(8\right)}^2+6\left(8\right)-112\stackrel{?}{=}0 \\ 0=0✓ \end{gathered}$$

Therefore, the obtained solution is correct. As the obtained solution completely matches with option F, option F is the required answer.