use the zero product property to find the solutions to the equation $x^{2}-9 = 16$.\n$x=-3$ or $x =…

Explanation:

Step1: Rearrange the equation

First, rewrite $x^{2}-9 = 16$ as $x^{2}-9 - 16=0$, so $x^{2}-25 = 0$.

Step2: Factor the left - hand side

Using the difference of squares formula $a^{2}-b^{2}=(a + b)(a - b)$, where $a = x$ and $b = 5$, we get $(x + 5)(x - 5)=0$.

Step3: Apply the zero - product property

If $ab = 0$, then either $a = 0$ or $b = 0$. So $x+5 = 0$ or $x - 5=0$.

Step4: Solve for x

For $x+5 = 0$, we have $x=-5$; for $x - 5=0$, we have $x = 5$.

Answer:

$x=-5$ or $x = 5$