Solve by Factoring x^2-144=0

$x^{2} - 144 = 0$

Step 1

Rewrite $144$ as $12^{2}$ .

$x^{2} - 12^{2} = 0$

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 12$ .

$(x + 12) (x - 12) = 0$

Step 3

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x + 12 = 0$

$x - 12 = 0$

Step 4

Set $x + 12$ equal to $0$ and solve for $x$ .

Set $x + 12$ equal to $0$ .

$x + 12 = 0$

Subtract $12$ from both sides of the equation.

$x = - 12$

Step 5

Set $x - 12$ equal to $0$ and solve for $x$ .

Set $x - 12$ equal to $0$ .

$x - 12 = 0$

Add $12$ to both sides of the equation.

$x = 12$

Step 6

The final solution is all the values that make $(x + 12) (x - 12) = 0$ true.

$x = - 12, 12$