Precalculus Examples

$- 300 + x - 300 \cos (30) = 0$

Step 1

Simplify each term.

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Step 1.1

The exact value of $\cos (30)$ is $\frac{\sqrt{3}}{2}$ .

$- 300 + x - 300 \frac{\sqrt{3}}{2} = 0$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $- 300$ .

$- 300 + x + 2 (- 150) \frac{\sqrt{3}}{2} = 0$

Step 1.2.2

Cancel the common factor.

$- 300 + x + 2 \cdot - 150 \frac{\sqrt{3}}{2} = 0$

Step 1.2.3

Rewrite the expression.

$- 300 + x - 150 \sqrt{3} = 0$

Step 2

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

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Step 2.1

Add $300$ to both sides of the equation.

$x - 150 \sqrt{3} = 300$

Step 2.2

Add $150 \sqrt{3}$ to both sides of the equation.

$x = 300 + 150 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = 300 + 150 \sqrt{3}$

Decimal Form:

$x = 559.80762113 \dots$