Solve sqrt{3}X-x-4/tan36^circ=164

$$\sqrt { 3 } X - \frac { x - 4 } { \tan 36 ^ { \circ } } = 164$$

Solve for X

$$X=\frac{4\sqrt{3}\left(312500000000000x+35985304560274741\right)}{2724534480020103}$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\sqrt{3} X - \frac{x - 4}{0.7265425280053608} = 164$$

Divide each term of x-4 by 0.7265425280053608 to get \frac{x}{0.7265425280053608}+\frac{-4}{0.7265425280053608}.

$$\sqrt{3}X-\left(\frac{x}{0.7265425280053608}+\frac{-4}{0.7265425280053608}\right)=164$$

Expand \frac{-4}{0.7265425280053608} by multiplying both numerator and the denominator by 10000000000000000.

$$\sqrt{3}X-\left(\frac{x}{0.7265425280053608}+\frac{-40000000000000000}{7265425280053608}\right)=164$$

Reduce the fraction \frac{-40000000000000000}{7265425280053608} to lowest terms by extracting and canceling out 8.

$$\sqrt{3}X-\left(\frac{x}{0.7265425280053608}-\frac{5000000000000000}{908178160006701}\right)=164$$

To find the opposite of \frac{x}{0.7265425280053608}-\frac{5000000000000000}{908178160006701}, find the opposite of each term.

$$\sqrt{3}X-\frac{x}{0.7265425280053608}+\frac{5000000000000000}{908178160006701}=164$$

Add \frac{x}{0.7265425280053608} to both sides.

$$\sqrt{3}X+\frac{5000000000000000}{908178160006701}=164+\frac{x}{0.7265425280053608}$$

Subtract \frac{5000000000000000}{908178160006701} from both sides.

$$\sqrt{3}X=164+\frac{x}{0.7265425280053608}-\frac{5000000000000000}{908178160006701}$$

Subtract \frac{5000000000000000}{908178160006701} from 164 to get \frac{143941218241098964}{908178160006701}.

$$\sqrt{3}X=\frac{143941218241098964}{908178160006701}+\frac{x}{0.7265425280053608}$$

The equation is in standard form.

$$\sqrt{3}X=\frac{1250000000000000x+143941218241098964}{908178160006701}$$

Divide both sides by \sqrt{3}.

$$\frac{\sqrt{3}X}{\sqrt{3}}=\frac{1250000000000000x+143941218241098964}{908178160006701\sqrt{3}}$$

Dividing by \sqrt{3} undoes the multiplication by \sqrt{3}.

$$X=\frac{1250000000000000x+143941218241098964}{908178160006701\sqrt{3}}$$

Divide \frac{143941218241098964+1250000000000000x}{908178160006701} by \sqrt{3}.

$$X=\frac{4\sqrt{3}\left(312500000000000x+35985304560274741\right)}{2724534480020103}$$

Solve for x

$$x=\frac{908178160006701\sqrt{3}X}{1250000000000000}-115.1529745928791712$$