Основы мат. анализа Примеры

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

Step 1

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 $0$ .

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

Step 2

Simplify.

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Step 2.1

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

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Step 2.1.1

Apply the distributive property.

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

Step 2.1.2

Apply the distributive property.

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

Step 2.1.3

Apply the distributive property.

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

Step 2.2

Simplify terms.

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Step 2.2.1

Combine the opposite terms in $x \cdot x + x \cdot 4 - 4 x - 4 \cdot 4$ .

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Step 2.2.1.1

Reorder the factors in the terms $x \cdot 4$ and $- 4 x$ .

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

Step 2.2.1.2

Subtract $4 x$ from $4 x$ .

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

Step 2.2.1.3

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

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

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 $4$ .

$x^{2} - 16 = 0$