Precalculus Examples

$x = 4$ , $x = - 4$

Since the roots of an equation are the points where the solution is $0$ , set each root as a factor of the equation that equals $0$ .

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

Simplify.

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

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Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

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Simplify each term.

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Multiply $x$ by $x$ .

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

Move $4$ to the left of $x$ .

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

Multiply $- 4$ by $4$ .

$x^{2} + 4 x - 4 x - 16 = 0$

Subtract $4 x$ from $4 x$ .

$x^{2} + 0 - 16 = 0$

Add $x^{2}$ and $0$ .

$x^{2} - 16 = 0$

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