Q. 25 - Precalculus Enhanced with Graphing Utilities

Question

In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.

$\left(x+7\right)\left(x-1\right)={\left(x+1\right)}^2$

Step-by-Step Solution

Answer

The required solution is $x=2$ and the graph of the solution is given below:

Step 1. Given information.

We have:

$\left(x+7\right)\left(x-1\right)={\left(x+1\right)}^2$

Step 2. Solve the equation algebraically.

The equation is $\left(x+7\right)\left(x-1\right)={\left(x+1\right)}^2.$

Expand:

$x^2+6x-7=x^2+2x+1$

Add $7$ to both sides:

$$\begin{gathered} x^2+6x-7+7=x^2+2x+1+7 \\ {x}^2+6x=x^2+2x+8 \end{gathered}$$

Subtract $x^2+2x$ to both sides:

$$\begin{gathered} x^2+6x-\left(x^2+2x\right)=x^2+2x+8-\left(x^2+2x\right) \\ 4x=8 \\ \frac{4x}{4}=\frac{8}{4} \\ x=2 \end{gathered}$$

Step 3. Verify the solution using a graphing utility.

The solution of the equation is $x=2.$

Draw the graph of the equation $\left(x+7\right)\left(x-1\right)={\left(x+1\right)}^2$ using the graphing utility: