Solve by Factoring 4=4+x^2-4

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

Step 1

Move all the expressions to the left side of the equation.

Subtract $4$ from both sides of the equation.

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

Subtract $x^{2}$ from both sides of the equation.

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

Add $4$ to both sides of the equation.

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

Step 2

Simplify $4 - 4 - x^{2} + 4$ .

Subtract $4$ from $4$ .

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

Subtract $x^{2}$ from $0$ .

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

Step 3

Rewrite $4$ as $2^{2}$ .

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

Step 4

Reorder $- x^{2}$ and $2^{2}$ .

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

Step 5

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

$(2 + x) (2 - x) = 0$

Step 6

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

$2 + x = 0$

$2 - x = 0$

Step 7

Set $2 + x$ equal to $0$ and solve for $x$ .

Set $2 + x$ equal to $0$ .

$2 + x = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 8

Set $2 - x$ equal to $0$ and solve for $x$ .

Set $2 - x$ equal to $0$ .

$2 - x = 0$

Solve $2 - x = 0$ for $x$ .

Subtract $2$ from both sides of the equation.

$- x = - 2$

Divide each term in $- x = - 2$ by $- 1$ and simplify.

Divide each term in $- x = - 2$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 2}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 2}{- 1}$

Simplify the right side.

Divide $- 2$ by $- 1$ .

$x = 2$

Step 9

The final solution is all the values that make $(2 + x) (2 - x) = 0$ true.

$x = - 2, 2$

Solve by Factoring 4=4+x^2-4

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