ដោះស្រាយ w=w+5/512(sin14)

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

ដោះស្រាយសម្រាប់ w

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

ជំហានសម្រាប់ការដោះស្រាយសមីការលីនេអ៊ែរ

Evaluate trigonometric functions in the problem

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

ចែកតួនីមួយៗនៃ w+5 នឹង 512 ដើម្បីទទួលបាន \frac{1}{512}w+\frac{5}{512}។

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

ប្រើលក្ខណៈបំបែក​ដើម្បីគុណ \frac{1}{512}w+\frac{5}{512} នឹង 0.24192189559966773។

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

បម្លែងចំនួនទសភាគ 0.24192189559966773 ទៅជាប្រភាគ \frac{24192189559966773}{10000000000}។ កាត់បន្ថយប្រភាគ \frac{24192189559966773}{10000000000} ទៅតួដែលតូចបំផុតដោយ​ដក និងលុបចេញ 1។

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

គុណ \frac{1}{512} ដង \frac{24192189559966773}{100000000000000000} ដោយការគុណភាគយក​ចំនួនដងនៃភាគយក និងភាគបែងចំនួនដងនៃភាគបែង។

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

ធ្វើផល​គុណនៅក្នុងប្រភាគ \frac{1\times 24192189559966773}{512\times 100000000000000000}។

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

បម្លែងចំនួនទសភាគ 0.24192189559966773 ទៅជាប្រភាគ \frac{24192189559966773}{10000000000}។ កាត់បន្ថយប្រភាគ \frac{24192189559966773}{10000000000} ទៅតួដែលតូចបំផុតដោយ​ដក និងលុបចេញ 1។

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

គុណ \frac{5}{512} ដង \frac{24192189559966773}{100000000000000000} ដោយការគុណភាគយក​ចំនួនដងនៃភាគយក និងភាគបែងចំនួនដងនៃភាគបែង។

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

ធ្វើផល​គុណនៅក្នុងប្រភាគ \frac{5\times 24192189559966773}{512\times 100000000000000000}។

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

កាត់បន្ថយប្រភាគ \frac{120960947799833865}{51200000000000000000} ទៅតួដែលតូចបំផុតដោយ​ដក និងលុបចេញ 5។

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

ដក \frac{24192189559966773}{51200000000000000000}w ពីជ្រុងទាំងពីរ។

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

បន្សំ w និង -\frac{24192189559966773}{51200000000000000000}w ដើម្បីបាន \frac{51175807810440033227}{51200000000000000000}w។

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

គុណ​ជ្រុងទាំងពីរនឹង \frac{51200000000000000000}{51175807810440033227}, ភាពផ្ទុយគ្នានៃ \frac{51175807810440033227}{51200000000000000000}។

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

គុណ \frac{24192189559966773}{10240000000000000000} ដង \frac{51200000000000000000}{51175807810440033227} ដោយការគុណភាគយក​ចំនួនដងនៃភាគយក និងភាគបែងចំនួនដងនៃភាគបែង។

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

ធ្វើផល​គុណនៅក្នុងប្រភាគ \frac{24192189559966773\times 51200000000000000000}{10240000000000000000\times 51175807810440033227}។

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

កាត់បន្ថយប្រភាគ \frac{1238640105470298777600000000000000000}{524040271978905940244480000000000000000} ទៅតួដែលតូចបំផុតដោយ​ដក និងលុបចេញ 10240000000000000000។

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