Solve 500sqrt{3}+x=500+xtan75^circ

$$500 \sqrt { 3 } + x = 500 + x \tan 75 ^ { \circ }$$

Solve for x_3

$$x_{3}=\frac{1250000000000000x+625000000000000000\sqrt{3}-625000000000000000}{915063509461097}$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$500 \sqrt{3} + x = 500 + x 3.7320508075688776$$

Swap sides so that all variable terms are on the left hand side.

$$500+x_{3}\times 0.7320508075688776=500\sqrt{3}+x$$

Subtract 500 from both sides.

$$x_{3}\times 0.7320508075688776=500\sqrt{3}+x-500$$

The equation is in standard form.

$$0.7320508075688776x_{3}=x+500\sqrt{3}-500$$

Divide both sides of the equation by 0.7320508075688776, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{0.7320508075688776x_{3}}{0.7320508075688776}=\frac{x+500\sqrt{3}-500}{0.7320508075688776}$$

Dividing by 0.7320508075688776 undoes the multiplication by 0.7320508075688776.

$$x_{3}=\frac{x+500\sqrt{3}-500}{0.7320508075688776}$$

Divide 500\sqrt{3}+x-500 by 0.7320508075688776 by multiplying 500\sqrt{3}+x-500 by the reciprocal of 0.7320508075688776.

$$x_{3}=\frac{1250000000000000x+625000000000000000\sqrt{3}-625000000000000000}{915063509461097}$$

Solve for x

$$x=\frac{915063509461097x_{3}}{1250000000000000}+500-500\sqrt{3}$$