Solve w=w+5/512(sin14)

$$w = \frac { w + 5 } { 512 } ( \sin 14 )$$

Solve for w

$$w=\frac{120960947799833865}{51175807810440033227}\approx 0.002363635$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$w = \frac{w + 5}{512} 0.24192189559966773$$

Divide each term of w+5 by 512 to get \frac{1}{512}w+\frac{5}{512}.

$$w=\left(\frac{1}{512}w+\frac{5}{512}\right)\times 0.24192189559966773$$

Use the distributive property to multiply \frac{1}{512}w+\frac{5}{512} by 0.24192189559966773.

$$w=\frac{1}{512}w\times 0.24192189559966773+\frac{5}{512}\times 0.24192189559966773$$

Convert decimal number 0.24192189559966773 to fraction \frac{24192189559966773}{10000000000}. Reduce the fraction \frac{24192189559966773}{10000000000} to lowest terms by extracting and canceling out 1.

$$w=\frac{1}{512}w\times \frac{24192189559966773}{100000000000000000}+\frac{5}{512}\times 0.24192189559966773$$

Multiply \frac{1}{512} times \frac{24192189559966773}{100000000000000000} by multiplying numerator times numerator and denominator times denominator.

$$w=\frac{1\times 24192189559966773}{512\times 100000000000000000}w+\frac{5}{512}\times 0.24192189559966773$$

Do the multiplications in the fraction \frac{1\times 24192189559966773}{512\times 100000000000000000}.

$$w=\frac{24192189559966773}{51200000000000000000}w+\frac{5}{512}\times 0.24192189559966773$$

Convert decimal number 0.24192189559966773 to fraction \frac{24192189559966773}{10000000000}. Reduce the fraction \frac{24192189559966773}{10000000000} to lowest terms by extracting and canceling out 1.

$$w=\frac{24192189559966773}{51200000000000000000}w+\frac{5}{512}\times \frac{24192189559966773}{100000000000000000}$$

Multiply \frac{5}{512} times \frac{24192189559966773}{100000000000000000} by multiplying numerator times numerator and denominator times denominator.

$$w=\frac{24192189559966773}{51200000000000000000}w+\frac{5\times 24192189559966773}{512\times 100000000000000000}$$

Do the multiplications in the fraction \frac{5\times 24192189559966773}{512\times 100000000000000000}.

$$w=\frac{24192189559966773}{51200000000000000000}w+\frac{120960947799833865}{51200000000000000000}$$

Reduce the fraction \frac{120960947799833865}{51200000000000000000} to lowest terms by extracting and canceling out 5.

$$w=\frac{24192189559966773}{51200000000000000000}w+\frac{24192189559966773}{10240000000000000000}$$

Subtract \frac{24192189559966773}{51200000000000000000}w from both sides.

$$w-\frac{24192189559966773}{51200000000000000000}w=\frac{24192189559966773}{10240000000000000000}$$

Combine w and -\frac{24192189559966773}{51200000000000000000}w to get \frac{51175807810440033227}{51200000000000000000}w.

$$\frac{51175807810440033227}{51200000000000000000}w=\frac{24192189559966773}{10240000000000000000}$$

Multiply both sides by \frac{51200000000000000000}{51175807810440033227}, the reciprocal of \frac{51175807810440033227}{51200000000000000000}.

$$w=\frac{24192189559966773}{10240000000000000000}\times \frac{51200000000000000000}{51175807810440033227}$$

Multiply \frac{24192189559966773}{10240000000000000000} times \frac{51200000000000000000}{51175807810440033227} by multiplying numerator times numerator and denominator times denominator.

$$w=\frac{24192189559966773\times 51200000000000000000}{10240000000000000000\times 51175807810440033227}$$

Do the multiplications in the fraction \frac{24192189559966773\times 51200000000000000000}{10240000000000000000\times 51175807810440033227}.

$$w=\frac{1238640105470298777600000000000000000}{524040271978905940244480000000000000000}$$

Reduce the fraction \frac{1238640105470298777600000000000000000}{524040271978905940244480000000000000000} to lowest terms by extracting and canceling out 10240000000000000000.

$$w=\frac{120960947799833865}{51175807810440033227}$$