Solve Using the Quadratic Formula (x-9)(x+9)=0

$(x - 9) (x + 9) = 0$

Step 1

Simplify the left side.

Simplify $(x - 9) (x + 9)$ .

Expand $(x - 9) (x + 9)$ using the FOIL Method.

Apply the distributive property.

$x (x + 9) - 9 (x + 9) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 9 - 9 (x + 9) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 9 - 9 x - 9 \cdot 9 = 0$

Simplify terms.

Combine the opposite terms in $x \cdot x + x \cdot 9 - 9 x - 9 \cdot 9$ .

Reorder the factors in the terms $x \cdot 9$ and $- 9 x$ .

$x \cdot x + 9 x - 9 x - 9 \cdot 9 = 0$

Subtract $9 x$ from $9 x$ .

$x \cdot x + 0 - 9 \cdot 9 = 0$

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

$x \cdot x - 9 \cdot 9 = 0$

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} - 9 \cdot 9 = 0$

Multiply $- 9$ by $9$ .

$x^{2} - 81 = 0$

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 $c = - 81$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot - 81)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot - 81}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 81$ .

Multiply $- 4$ by $1$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 81}}{2 \cdot 1}$

Multiply $- 4$ by $- 81$ .

$x = \frac{0 \pm \sqrt{0 + 324}}{2 \cdot 1}$

Add $0$ and $324$ .

$x = \frac{0 \pm \sqrt{324}}{2 \cdot 1}$

Rewrite $324$ as $18^{2}$ .

$x = \frac{0 \pm \sqrt{18^{2}}}{2 \cdot 1}$

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

$x = \frac{0 \pm 18}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{0 \pm 18}{2}$

Simplify $\frac{0 \pm 18}{2}$ .

$x = \pm 9$

Step 5

The final answer is the combination of both solutions.

$x = 9, - 9$

Solve Using the Quadratic Formula (x-9)(x+9)=0

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