Trigonometry Examples

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

Step 1

Factor the left side of the equation.

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Step 1.1

Factor $4$ out of $4 x^{2} - 16 x + 16$ .

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Step 1.1.1

Factor $4$ out of $4 x^{2}$ .

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

Step 1.1.2

Factor $4$ out of $- 16 x$ .

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

Step 1.1.3

Factor $4$ out of $16$ .

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

Step 1.1.4

Factor $4$ out of $4 x^{2} + 4 (- 4 x)$ .

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

Step 1.1.5

Factor $4$ out of $4 (x^{2} - 4 x) + 4 \cdot 4$ .

$4 (x^{2} - 4 x + 4) = 0$

Step 1.2

Factor using the perfect square rule.

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Step 1.2.1

Rewrite $4$ as $2^{2}$ .

$4 (x^{2} - 4 x + 2^{2}) = 0$

Step 1.2.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$4 x = 2 \cdot x \cdot 2$

Step 1.2.3

Rewrite the polynomial.

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

Step 1.2.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 2$ .

$4 {(x - 2)}^{2} = 0$

Step 2

Divide each term in $4 {(x - 2)}^{2} = 0$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 {(x - 2)}^{2} = 0$ by $4$ .

$\frac{4 {(x - 2)}^{2}}{4} = \frac{0}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 {(x - 2)}^{2}}{4} = \frac{0}{4}$

Step 2.2.1.2

Divide ${(x - 2)}^{2}$ by $1$ .

${(x - 2)}^{2} = \frac{0}{4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $0$ by $4$ .

${(x - 2)}^{2} = 0$

Step 3

Set the $x - 2$ equal to $0$ .

$x - 2 = 0$

Step 4

Add $2$ to both sides of the equation.

$x = 2$