Answer
x=-5,5
Work Step by Step
In order to solve the equation $x^{2}$-25=0 we will factor the left side of the equation by applying the rule that states
$a^{2}$-$b^{2}$=(a+b)(a-b)
If we set $a^{2}$=$x^{2}$
and $b^{2}$=25, we can solve for a and b.
$a^{2}$=$x^{2}$
After we square root both sides of the equation, we will get
a=x
$b^{2}$=25
After we square root both sides of equation, we will go
b=5
Therefore,
$x^{2}$-25=(x+5)(x-5)
And if $x^{2}$-25=0, then we can set x+5=0 and x-5=0
For x+5=0, we can solve for x by subtracting 5 from both sides of the equation, and getting
x=-5
For x-5=0, we can solve for x by adding 5 to both sides of the equation, and getting
x=5
