Chapter 8.6, Problem 73SR

To determine

To Evaluate: Evaluate the equation and check the answer.

Answer to Problem 73SR

The solution is: $x=-2,1$ .

Explanation of Solution

Given information:

The equation is:

  $14x^2+14x=28$

Calculation:

Here the equation is:

  $14x^2+14x=28$

The strategy is to solve the equation and to check the answer.

The equation can be solved as below:

  $\begin{array}{r}\hfill 14x^2+14x=28\\ \hfill 14x^2+14x-28=0\\ \hfill 14\left(x^2+x-2\right)=0\\ \hfill x^2+2x-x-2=0\\ \hfill x(x+2)-1(x+2)=0\\ \hfill (x+2)(x-1)=0\\ \hfill x+2=0,x-1=0\\ \hfill x=-2,x=1\end{array}$

Hence, the solution is: $x=-2,1$ .

Check:

Put $x=-2$ in the equation;

  $\begin{array}{r}\hfill 14{(-2)}^2+14(-2)=28\\ \hfill 14\cdot 4-28=28\\ \hfill 56-28=28\\ \hfill 28=28\end{array}$

Again, put $x=1$ in the equation;

  $14{(1)}^2+14(1)=28$

  $\begin{array}{cc}14+14& =28\\ 28& =28\end{array}$

Hence, the solution is correct.