Q. 26 - Precalculus Enhanced with Graphing Utilities

Question

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

$\left(x+2\right)\left(x-3\right)={\left(x-3\right)}^2$

Step-by-Step Solution

Answer

The required solution is $x=3$ and the graph of the solution is given below:

Step 1. Given information.

We have:

$\left(x+2\right)\left(x-3\right)={\left(x-3\right)}^2$

Step 2. Solve the equation algebraically.

The solution of the equation is $\left(x+2\right)\left(x-3\right)={\left(x-3\right)}^2$.

Expand:

$x^2-x-6=x^2-6x+9$

Add $6$ to both sides:

$$\begin{gathered} x^2-x-6+6=x^2-6x+9+6 \\ {x}^2-x=x^2-6x+15 \end{gathered}$$

Subtract $x^2-6x$ from both sides:

$$\begin{gathered} x^2-x-\left(x^2-6x\right)=x^2-6x+15-\left(x^2-6x\right) \\ 5x=15 \\ \frac{5x}{5}=\frac{15}{5} \\ x=3 \end{gathered}$$

Step 3. Verify the solution using a graphing utility.

The solution of the equation is $x=3.$

Draw the graph of the equation $\left(x+2\right)\left(x-3\right)={\left(x-3\right)}^2$ using the graphing utility: