Solve Using the Quadratic Formula (x-2)(x+2)=0

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

Step 1

Simplify the left side.

Simplify $(x - 2) (x + 2)$ .

Expand $(x - 2) (x + 2)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

$x \cdot x + x \cdot 2 - 2 x - 2 \cdot 2 = 0$

Simplify terms.

Combine the opposite terms in $x \cdot x + x \cdot 2 - 2 x - 2 \cdot 2$ .

Reorder the factors in the terms $x \cdot 2$ and $- 2 x$ .

$x \cdot x + 2 x - 2 x - 2 \cdot 2 = 0$

Subtract $2 x$ from $2 x$ .

$x \cdot x + 0 - 2 \cdot 2 = 0$

Add $x \cdot x$ and $0$ .

$x \cdot x - 2 \cdot 2 = 0$

Simplify each term.

Multiply $x$ by $x$ .

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

Multiply $- 2$ by $2$ .

$x^{2} - 4 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 1$ , $b = 0$ , and $c = - 4$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot - 4)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot - 4}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 4$ .

Multiply $- 4$ by $1$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 4}}{2 \cdot 1}$

Multiply $- 4$ by $- 4$ .

$x = \frac{0 \pm \sqrt{0 + 16}}{2 \cdot 1}$

Add $0$ and $16$ .

$x = \frac{0 \pm \sqrt{16}}{2 \cdot 1}$

Rewrite $16$ as $4^{2}$ .

$x = \frac{0 \pm \sqrt{4^{2}}}{2 \cdot 1}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{0 \pm 4}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{0 \pm 4}{2}$

Simplify $\frac{0 \pm 4}{2}$ .

$x = \pm 2$

Step 5

The final answer is the combination of both solutions.

$x = 2, - 2$

Solve Using the Quadratic Formula (x-2)(x+2)=0

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