Algebra Examples

$(x - 6) (x + 6) = 0$

Step 1

Simplify the left side.

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Step 1.1

Simplify $(x - 6) (x + 6)$ .

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Step 1.1.1

Expand $(x - 6) (x + 6)$ using the FOIL Method.

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Step 1.1.1.1

Apply the distributive property.

$x (x + 6) - 6 (x + 6) = 0$

Step 1.1.1.2

Apply the distributive property.

$x \cdot x + x \cdot 6 - 6 (x + 6) = 0$

Step 1.1.1.3

Apply the distributive property.

$x \cdot x + x \cdot 6 - 6 x - 6 \cdot 6 = 0$

Step 1.1.2

Simplify terms.

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Step 1.1.2.1

Combine the opposite terms in $x \cdot x + x \cdot 6 - 6 x - 6 \cdot 6$ .

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Step 1.1.2.1.1

Reorder the factors in the terms $x \cdot 6$ and $- 6 x$ .

$x \cdot x + 6 x - 6 x - 6 \cdot 6 = 0$

Step 1.1.2.1.2

Subtract $6 x$ from $6 x$ .

$x \cdot x + 0 - 6 \cdot 6 = 0$

Step 1.1.2.1.3

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

$x \cdot x - 6 \cdot 6 = 0$

Step 1.1.2.2

Simplify each term.

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Step 1.1.2.2.1

Multiply $x$ by $x$ .

$x^{2} - 6 \cdot 6 = 0$

Step 1.1.2.2.2

Multiply $- 6$ by $6$ .

$x^{2} - 36 = 0$

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 $c = - 36$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot - 36)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot - 36}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot - 36$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 36}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $- 36$ .

$x = \frac{0 \pm \sqrt{0 + 144}}{2 \cdot 1}$

Step 4.1.3

Add $0$ and $144$ .

$x = \frac{0 \pm \sqrt{144}}{2 \cdot 1}$

Step 4.1.4

Rewrite $144$ as $12^{2}$ .

$x = \frac{0 \pm \sqrt{12^{2}}}{2 \cdot 1}$

Step 4.1.5

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

$x = \frac{0 \pm 12}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$x = \frac{0 \pm 12}{2}$

Step 4.3

Simplify $\frac{0 \pm 12}{2}$ .

$x = \pm 6$

Step 5

The final answer is the combination of both solutions.

$x = 6, - 6$