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On line Solution of Monovariate Equation：
Input any unary equation directly, and then click the "Next" button to obtain the solution of the equation.
It supports equations that contain mathematical functions.
Input any unary equation directly, and then click the "Next" button to obtain the solution of the equation.
It supports equations that contain mathematical functions.
Current location：Equations > Monovariate Equation > The history of univariate equation calculation > Answer
Overview: 1 questions will be solved this time.Among them
☆1 equations
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Work: Find the solution of equation （28.5-20）/（30-28.5） = （a-1.005）/（0.8007-a） .
Question type: Equation
Solution:Original question:
| ( | 57 2 | − | 20 | ) | ÷ | ( | 30 | − | 57 2 | ) | = | ( | a | − | 201 200 | ) | ÷ | ( | 8007 10000 | − | a | ) |
| Multiply both sides of the equation by: | ( | 30 | − | 57 2 | ) | , | ( | 8007 10000 | − | a | ) |
| ( | 57 2 | − | 20 | ) | ( | 8007 10000 | − | a | ) | = | ( | a | − | 201 200 | ) | ( | 30 | − | 57 2 | ) |
57 2 | ( | 8007 10000 | − | a | ) | − | 20 | ( | 8007 10000 | − | a | ) | = | ( | a | − | 201 200 | ) | ( | 30 | − | 57 2 | ) |
57 2 | ( | 8007 10000 | − | a | ) | − | 20 | ( | 8007 10000 | − | a | ) | = | a | ( | 30 | − | 57 2 | ) | − | 201 200 | ( | 30 | − | 57 2 | ) |
57 2 | × | 8007 10000 | − | 57 2 | a | − | 20 | ( | 8007 10000 | − | a | ) | = | a | ( | 30 | − | 57 2 | ) | − | 201 200 | ( | 30 | − | 57 2 | ) |
57 2 | × | 8007 10000 | − | 57 2 | a | − | 20 | ( | 8007 10000 | − | a | ) | = | a | × | 30 | − | a | × | 57 2 | − | 201 200 | ( | 30 | − | 57 2 | ) |
456399 20000 | − | 57 2 | a | − | 20 | ( | 8007 10000 | − | a | ) | = | a | × | 30 | − | a | × | 57 2 | − | 201 200 | ( | 30 | − | 57 2 | ) |
456399 20000 | − | 57 2 | a | − | 20 | ( | 8007 10000 | − | a | ) | = | 3 2 | a | − | 201 200 | ( | 30 | − | 57 2 | ) |
456399 20000 | − | 57 2 | a | − | 20 | × | 8007 10000 | + | 20 | a | = | 3 2 | a | − | 201 200 | ( | 30 | − | 57 2 | ) |
456399 20000 | − | 57 2 | a | − | 20 | × | 8007 10000 | + | 20 | a | = | 3 2 | a | − | 201 200 | × | 30 | + | 201 200 | × | 57 2 |
456399 20000 | − | 57 2 | a | − | 8007 500 | + | 20 | a | = | 3 2 | a | − | 603 20 | + | 11457 400 |
136119 20000 | − | 17 2 | a | = | 3 2 | a | − | 603 400 |
Transposition :
| - | 17 2 | a | − | 3 2 | a | = | - | 603 400 | − | 136119 20000 |
Combine the items on the left of the equation:
| - | 10 | a | = | - | 603 400 | − | 136119 20000 |
Combine the items on the right of the equation:
| - | 10 | a | = | - | 166269 20000 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
166269 20000 | = | 10 | a |
If the left side of the equation is equal to the right side, then the right side must also be equal to the left side, that is :
| 10 | a | = | 166269 20000 |
The coefficient of the unknown number is reduced to 1 :
| a | = | 166269 20000 | ÷ | 10 |
| = | 166269 20000 | × | 1 10 |
We obtained :
| a | = | 166269 200000 |
Convert the result to decimal form :
| a | = | 0.831345 |