Precalculus Examples

x = 4

$x = 4$ ,

x = - 4

$x = - 4$

Step 1

Since the roots of an equation are the points where the solution is

0

$0$ , set each root as a factor of the equation that equals

0

$0$ .

(x - 4) (x - (- 4)) = 0

$(x - 4) (x - (- 4)) = 0$

Step 2

Simplify.

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Step 2.1

Expand

(x - 4) (x + 4)

$(x - 4) (x + 4)$ using the FOIL Method.

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Step 2.1.1

Apply the distributive property.

x (x + 4) - 4 (x + 4) = 0

$x (x + 4) - 4 (x + 4) = 0$

Step 2.1.2

Apply the distributive property.

x \cdot x + x \cdot 4 - 4 (x + 4) = 0

$x \cdot x + x \cdot 4 - 4 (x + 4) = 0$

Step 2.1.3

Apply the distributive property.

x \cdot x + x \cdot 4 - 4 x - 4 \cdot 4 = 0

$x \cdot x + x \cdot 4 - 4 x - 4 \cdot 4 = 0$

x \cdot x + x \cdot 4 - 4 x - 4 \cdot 4 = 0

$x \cdot x + x \cdot 4 - 4 x - 4 \cdot 4 = 0$

Step 2.2

Simplify terms.

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Step 2.2.1

Combine the opposite terms in

x \cdot x + x \cdot 4 - 4 x - 4 \cdot 4

$x \cdot x + x \cdot 4 - 4 x - 4 \cdot 4$ .

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Step 2.2.1.1

Reorder the factors in the terms

x \cdot 4

$x \cdot 4$ and

- 4 x

$- 4 x$ .

x \cdot x + 4 x - 4 x - 4 \cdot 4 = 0

$x \cdot x + 4 x - 4 x - 4 \cdot 4 = 0$

Step 2.2.1.2

Subtract

4 x

$4 x$ from

4 x

$4 x$ .

x \cdot x + 0 - 4 \cdot 4 = 0

$x \cdot x + 0 - 4 \cdot 4 = 0$

Step 2.2.1.3

Add

x \cdot x

$x \cdot x$ and

0

$0$ .

x \cdot x - 4 \cdot 4 = 0

$x \cdot x - 4 \cdot 4 = 0$

x \cdot x - 4 \cdot 4 = 0

$x \cdot x - 4 \cdot 4 = 0$

Step 2.2.2

Simplify each term.

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Step 2.2.2.1

Multiply

$x$ by

$x$ .

$x^{2} - 4 \cdot 4 = 0$

Step 2.2.2.2

Multiply

$- 4$ by

$4$ .

$x^{2} - 16 = 0$

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