Algebra Examples

x^{2} - 16 = 0

$x^{2} - 16 = 0$

Step 1

Rewrite

16

$16$ as

4^{2}

$4^{2}$ .

x^{2} - 4^{2} = 0

$x^{2} - 4^{2} = 0$

Step 2

Since both terms are perfect squares, factor using the difference of squares formula,

a^{2} - b^{2} = (a + b) (a - b)

$a^{2} - b^{2} = (a + b) (a - b)$ where

a = x

$a = x$ and

b = 4

$b = 4$ .

(x + 4) (x - 4) = 0

$(x + 4) (x - 4) = 0$

Step 3

If any individual factor on the left side of the equation is equal to

0

$0$ , the entire expression will be equal to

0

$0$ .

x + 4 = 0

$x + 4 = 0$

x - 4 = 0

$x - 4 = 0$

Step 4

Set

x + 4

$x + 4$ equal to

0

$0$ and solve for

x

$x$ .

Tap for more steps...

Step 4.1

Set

x + 4

$x + 4$ equal to

0

$0$ .

x + 4 = 0

$x + 4 = 0$

Step 4.2

Subtract

4

$4$ from both sides of the equation.

x = - 4

$x = - 4$

x = - 4

$x = - 4$

Step 5

Set

x - 4

$x - 4$ equal to

0

$0$ and solve for

x

$x$ .

Tap for more steps...

Step 5.1

Set

x - 4

$x - 4$ equal to

0

$0$ .

x - 4 = 0

$x - 4 = 0$

Step 5.2

Add

4

$4$ to both sides of the equation.

x = 4

$x = 4$

x = 4

$x = 4$

Step 6

The final solution is all the values that make

(x + 4) (x - 4) = 0

$(x + 4) (x - 4) = 0$ true.

x = - 4, 4

$x = - 4, 4$