Finite Math Examples

$(9 x + 3) (9 x - 3)$

Step 1

Set $(9 x + 3) (9 x - 3)$ equal to $0$ .

$(9 x + 3) (9 x - 3) = 0$

Step 2

Simplify the left side.

Tap for more steps...

Step 2.1

Simplify $(9 x + 3) (9 x - 3)$ .

Tap for more steps...

Step 2.1.1

Expand $(9 x + 3) (9 x - 3)$ using the FOIL Method.

Tap for more steps...

Step 2.1.1.1

Apply the distributive property.

$9 x (9 x - 3) + 3 (9 x - 3) = 0$

Step 2.1.1.2

Apply the distributive property.

$9 x (9 x) + 9 x \cdot - 3 + 3 (9 x - 3) = 0$

Step 2.1.1.3

Apply the distributive property.

$9 x (9 x) + 9 x \cdot - 3 + 3 (9 x) + 3 \cdot - 3 = 0$

Step 2.1.2

Simplify terms.

Tap for more steps...

Step 2.1.2.1

Combine the opposite terms in $9 x (9 x) + 9 x \cdot - 3 + 3 (9 x) + 3 \cdot - 3$ .

Tap for more steps...

Step 2.1.2.1.1

Reorder the factors in the terms $9 x \cdot - 3$ and $3 (9 x)$ .

$9 x (9 x) - 3 \cdot 9 x + 3 \cdot 9 x + 3 \cdot - 3 = 0$

Step 2.1.2.1.2

Add $- 3 \cdot 9 x$ and $3 \cdot 9 x$ .

$9 x (9 x) + 0 + 3 \cdot - 3 = 0$

Step 2.1.2.1.3

Add $9 x (9 x)$ and $0$ .

$9 x (9 x) + 3 \cdot - 3 = 0$

Step 2.1.2.2

Simplify each term.

Tap for more steps...

Step 2.1.2.2.1

Rewrite using the commutative property of multiplication.

$9 \cdot 9 x \cdot x + 3 \cdot - 3 = 0$

Step 2.1.2.2.2

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 2.1.2.2.2.1

Move $x$ .

$9 \cdot 9 (x \cdot x) + 3 \cdot - 3 = 0$

Step 2.1.2.2.2.2

Multiply $x$ by $x$ .

$9 \cdot 9 x^{2} + 3 \cdot - 3 = 0$

Step 2.1.2.2.3

Multiply $9$ by $9$ .

$81 x^{2} + 3 \cdot - 3 = 0$

Step 2.1.2.2.4

Multiply $3$ by $- 3$ .

$81 x^{2} - 9 = 0$

Step 3

Use the quadratic formula to find the solutions.

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

Step 4

Substitute the values $a = 81$ , $b = 0$ , and $c = - 9$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (81 \cdot - 9)}}{2 \cdot 81}$

Step 5

Simplify.

Tap for more steps...

Step 5.1

Simplify the numerator.

Tap for more steps...

Step 5.1.1

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 81 \cdot - 9}}{2 \cdot 81}$

Step 5.1.2

Multiply $- 4 \cdot 81 \cdot - 9$ .

Tap for more steps...

Step 5.1.2.1

Multiply $- 4$ by $81$ .

$x = \frac{0 \pm \sqrt{0 - 324 \cdot - 9}}{2 \cdot 81}$

Step 5.1.2.2

Multiply $- 324$ by $- 9$ .

$x = \frac{0 \pm \sqrt{0 + 2916}}{2 \cdot 81}$

Step 5.1.3

Add $0$ and $2916$ .

$x = \frac{0 \pm \sqrt{2916}}{2 \cdot 81}$

Step 5.1.4

Rewrite $2916$ as $54^{2}$ .

$x = \frac{0 \pm \sqrt{54^{2}}}{2 \cdot 81}$

Step 5.1.5

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

$x = \frac{0 \pm 54}{2 \cdot 81}$

Step 5.2

Multiply $2$ by $81$ .

$x = \frac{0 \pm 54}{162}$

Step 5.3

Simplify $\frac{0 \pm 54}{162}$ .

$x = \frac{\pm 1}{3}$

Step 6

The final answer is the combination of both solutions.

$x = \frac{1}{3}, - \frac{1}{3}$