Trigonometry Examples

$6^{2} \cdot 10^{2} = x^{2}$

Step 1

Rewrite the equation as $x^{2} = 6^{2} \cdot 10^{2}$ .

$x^{2} = 6^{2} \cdot 10^{2}$

Step 2

Raise $6$ to the power of $2$ .

$x^{2} = 36 \cdot 10^{2}$

Step 3

Move the decimal point in $36$ to the left by $1$ place and increase the power of $10^{2}$ by $1$ .

$x^{2} = 3.6 \cdot 10^{3}$

Step 4

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

$x = \pm \sqrt{3.6 \cdot 10^{3}}$

Step 5

Simplify $\pm \sqrt{3.6 \cdot 10^{3}}$ .

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Step 5.1

Rewrite $3.6 \cdot 10^{3}$ as $0.36 \cdot 10^{4}$ .

$x = \pm \sqrt{0.36 \cdot 10^{4}}$

Step 5.2

Rewrite $\sqrt{0.36 \cdot 10^{4}}$ as $\sqrt{0.36} \cdot \sqrt{10^{4}}$ .

$x = \pm \sqrt{0.36} \cdot \sqrt{10^{4}}$

Step 5.3

Evaluate the root.

$x = \pm 0.6 \cdot \sqrt{10^{4}}$

Step 5.4

Rewrite $10^{4}$ as ${(10^{2})}^{2}$ .

$x = \pm 0.6 \cdot \sqrt{{(10^{2})}^{2}}$

Step 5.5

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

$x = \pm 0.6 \cdot 10^{2}$

Step 5.6

Move the decimal point in $0.6$ to the right by $1$ place and decrease the power of $10^{2}$ by $1$ .

$x = \pm 6 \cdot 10^{1}$

Step 6

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

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Step 6.1

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

$x = 6 \cdot 10^{1}$

Step 6.2

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

$x = - 6 \cdot 10^{1}$

Step 6.3

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

$x = 6 \cdot 10^{1}, - 6 \cdot 10^{1}$

Step 7

The result can be shown in multiple forms.

Scientific Notation:

$x = 6 \cdot 10^{1}, - 6 \cdot 10^{1}$

Expanded Form:

$x = 60, - 60$