Trigonometry Examples

${(3 x - 4)}^{2} = 16$

Step 1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$3 x - 4 = \pm \sqrt{16}$

Step 2

Simplify $\pm \sqrt{16}$ .

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Step 2.1

Rewrite $16$ as $4^{2}$ .

$3 x - 4 = \pm \sqrt{4^{2}}$

Step 2.2

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

$3 x - 4 = \pm 4$

Step 3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 3.1

First, use the positive value of the $\pm$ to find the first solution.

$3 x - 4 = 4$

Step 3.2

Move all terms not containing $x$ to the right side of the equation.

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Step 3.2.1

Add $4$ to both sides of the equation.

$3 x = 4 + 4$

Step 3.2.2

Add $4$ and $4$ .

$3 x = 8$

Step 3.3

Divide each term in $3 x = 8$ by $3$ and simplify.

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Step 3.3.1

Divide each term in $3 x = 8$ by $3$ .

$\frac{3 x}{3} = \frac{8}{3}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $3$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{8}{3}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{8}{3}$

Step 3.4

Next, use the negative value of the $\pm$ to find the second solution.

$3 x - 4 = - 4$

Step 3.5

Move all terms not containing $x$ to the right side of the equation.

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Step 3.5.1

Add $4$ to both sides of the equation.

$3 x = - 4 + 4$

Step 3.5.2

Add $- 4$ and $4$ .

$3 x = 0$

Step 3.6

Divide each term in $3 x = 0$ by $3$ and simplify.

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Step 3.6.1

Divide each term in $3 x = 0$ by $3$ .

$\frac{3 x}{3} = \frac{0}{3}$

Step 3.6.2

Simplify the left side.

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Step 3.6.2.1

Cancel the common factor of $3$ .

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Step 3.6.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{0}{3}$

Step 3.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{3}$

Step 3.6.3

Simplify the right side.

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Step 3.6.3.1

Divide $0$ by $3$ .

$x = 0$

Step 3.7

The complete solution is the result of both the positive and negative portions of the solution.

$x = \frac{8}{3}, 0$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{8}{3}, 0$

Decimal Form:

$x = 2.\overline{6}, 0$

Mixed Number Form:

$x = 2 \frac{2}{3}, 0$