Answer
The solutions are $m = 8$ and $m = -8$.
Work Step by Step
We can see that this equation features the difference of two squares. To factor an equation in the form $a^2 - b^2 = 0$, we use the following formula:
$a^2 - b^2 = (a - b)(a + b)$
Let's apply this formula to our equation, where $a = m$ and $b = 8$:
$(m - 8)(m + 8) = 0$
According to the zero product property, if the product of two factors equals $0$, then either factor can be $0$; therefore, we can set each of these factors equal to $0$ and solve:
$m - 8 = 0$ or $m + 8 = 0$
Add or subtract to solve:
$m = 8$ or $m = -8$
The solutions are $m = 8$ and $m = -8$.
To check our answer, we substitute each of these values into the original equation to see if the two sides equal one another:
$8^2 - 64 = 0$
Evaluate exponents first:
$64 - 64 = 0$
Subtract:
$0 = 0$
The two sides of the equation are equal to one another; therefore, this solution is correct.
Let's check the other solution:
$(-8)^2 - 64 = 0$
Evaluate exponents first:
$64 - 64 = 0$
Subtract:
$0 = 0$
The two sides of the equation are equal to one another; therefore, this solution is correct.