Exercise 69 Page 302

We want to solve the given equation by factoring.

Rewriting the Equation

To do so, we will first rewrite the equation to have everything on one side of the equals sign.

Applying the Difference of Two Squares

Do you notice that the expression on the left-hand side of the equation is a $\text{difference}$ of two $\text{perfect squares}?$ This can be factored using the difference of squares. To do so, we first need to express each term as a perfect square.

Expression	$x^2-36$
Rewrite as Perfect Squares	$x^2-6^2$
Apply the Formula	$(x+6)(x-6)$

Solving the Equation

Finally, to solve the equation, we will use the Zero Product Property. We found that the solutions to the equation are $\text{-}6$ and $6.$

Checking Our Answer

We can substitute our solutions back into the given equation and simplify to check if our answers are correct. We will start with $x=\text{-}6.$ Substituting and simplifying created a true statement, so we know that $x=\text{-}6$ is a solution of the equation. Let's move on to $x=6.$ Again, we created a true statement. Therefore, $x=6$ is indeed a solution of the equation.