Trigonometry Examples

$75 = \frac{1}{2} x^{2} \cdot 6$

Step 1

Rewrite the equation as $\frac{1}{2} x^{2} \cdot 6 = 75$ .

$\frac{1}{2} x^{2} \cdot 6 = 75$

Step 2

Simplify $\frac{1}{2} x^{2} \cdot 6$ .

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Step 2.1

Combine $\frac{1}{2}$ and $x^{2}$ .

$\frac{x^{2}}{2} \cdot 6 = 75$

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Factor $2$ out of $6$ .

$\frac{x^{2}}{2} \cdot (2 (3)) = 75$

Step 2.2.2

Cancel the common factor.

$\frac{x^{2}}{2} \cdot (2 \cdot 3) = 75$

Step 2.2.3

Rewrite the expression.

$x^{2} \cdot 3 = 75$

Step 2.3

Move $3$ to the left of $x^{2}$ .

$3 x^{2} = 75$

Step 3

Divide each term in $3 x^{2} = 75$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 x^{2} = 75$ by $3$ .

$\frac{3 x^{2}}{3} = \frac{75}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 x^{2}}{3} = \frac{75}{3}$

Step 3.2.1.2

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{75}{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $75$ by $3$ .

$x^{2} = 25$

Step 4

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

$x = \pm \sqrt{25}$

Step 5

Simplify $\pm \sqrt{25}$ .

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Step 5.1

Rewrite $25$ as $5^{2}$ .

$x = \pm \sqrt{5^{2}}$

Step 5.2

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

$x = \pm 5$

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.

$x = 5$

Step 6.2

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

$x = - 5$

Step 6.3

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

$x = 5, - 5$