Solve x(tan50)-x(tan15)=90

$$x ( \tan 50 ) - x ( \tan 15 ) = 90$$

Solve for x_0

$$x_{0}=\frac{639178641980700x_{1}-300000000000000000}{893163974770409}$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$x 1.19175359259421 - x 0.2679491924311227 = 90$$

Multiply -1 and 0.2679491924311227 to get -0.2679491924311227.

$$x_{1}\times 0.19175359259421-0.2679491924311227x_{0}=90$$

Subtract x_{1}\times 0.19175359259421 from both sides.

$$-0.2679491924311227x_{0}=90-x_{1}\times 0.19175359259421$$

The equation is in standard form.

$$-0.2679491924311227x_{0}=-\frac{19175359259421x_{1}}{100000000000000}+90$$

Divide both sides of the equation by -0.2679491924311227, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-0.2679491924311227x_{0}}{-0.2679491924311227}=\frac{-\frac{19175359259421x_{1}}{100000000000000}+90}{-0.2679491924311227}$$

Dividing by -0.2679491924311227 undoes the multiplication by -0.2679491924311227.

$$x_{0}=\frac{-\frac{19175359259421x_{1}}{100000000000000}+90}{-0.2679491924311227}$$

Divide 90-\frac{19175359259421x_{1}}{100000000000000} by -0.2679491924311227 by multiplying 90-\frac{19175359259421x_{1}}{100000000000000} by the reciprocal of -0.2679491924311227.

$$x_{0}=\frac{639178641980700x_{1}-300000000000000000}{893163974770409}$$

Solve for x_1

$$x_{1}=\frac{893163974770409x_{0}}{639178641980700}+\frac{1000000000000000}{2130595473269}$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$x 1.19175359259421 - x 0.2679491924311227 = 90$$

Add x_{0}\times 0.2679491924311227 to both sides.

$$x_{1}\times 0.19175359259421=90+x_{0}\times 0.2679491924311227$$

The equation is in standard form.

$$0.19175359259421x_{1}=\frac{2679491924311227x_{0}}{10000000000000000}+90$$

Divide both sides of the equation by 0.19175359259421, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{0.19175359259421x_{1}}{0.19175359259421}=\frac{\frac{2679491924311227x_{0}}{10000000000000000}+90}{0.19175359259421}$$

Dividing by 0.19175359259421 undoes the multiplication by 0.19175359259421.

$$x_{1}=\frac{\frac{2679491924311227x_{0}}{10000000000000000}+90}{0.19175359259421}$$

Divide 90+\frac{2679491924311227x_{0}}{10000000000000000} by 0.19175359259421 by multiplying 90+\frac{2679491924311227x_{0}}{10000000000000000} by the reciprocal of 0.19175359259421.

$$x_{1}=\frac{893163974770409x_{0}}{639178641980700}+\frac{1000000000000000}{2130595473269}$$