Solve Using the Quadratic Formula (x-1)(x+1)=0

$(x - 1) (x + 1) = 0$

Step 1

Simplify the left side.

Simplify $(x - 1) (x + 1)$ .

Expand $(x - 1) (x + 1)$ using the FOIL Method.

Apply the distributive property.

$x (x + 1) - 1 (x + 1) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 1 - 1 (x + 1) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 1 - 1 x - 1 \cdot 1 = 0$

Simplify terms.

Combine the opposite terms in $x \cdot x + x \cdot 1 - 1 x - 1 \cdot 1$ .

Reorder the factors in the terms $x \cdot 1$ and $- 1 x$ .

$x \cdot x + 1 x - 1 x - 1 \cdot 1 = 0$

Subtract $1 x$ from $1 x$ .

$x \cdot x + 0 - 1 \cdot 1 = 0$

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

$x \cdot x - 1 \cdot 1 = 0$

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} - 1 \cdot 1 = 0$

Multiply $- 1$ by $1$ .

$x^{2} - 1 = 0$

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 $c = - 1$ into the quadratic formula and solve for $x$ .

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

Step 4

Simplify.

Simplify the numerator.

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

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

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

Multiply $- 4$ by $1$ .

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

Multiply $- 4$ by $- 1$ .

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

Add $0$ and $4$ .

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

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

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

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

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

Multiply $2$ by $1$ .

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

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

$x = \pm 1$

Step 5

The final answer is the combination of both solutions.

$x = 1, - 1$

Solve Using the Quadratic Formula (x-1)(x+1)=0

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