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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
[ 1/1 Equation]
Work: Find the solution of equation (20-x)/15 = 2.8/(62.8-47.7) .
Question type: Equation
Solution:Original question:
| ( | 20 | − | x | ) | ÷ | 15 | = | 14 5 | ÷ | ( | 314 5 | − | 477 10 | ) |
| Multiply both sides of the equation by: | ( | 314 5 | − | 477 10 | ) |
| ( | 20 | − | x | ) | ÷ | 15 | × | ( | 314 5 | − | 477 10 | ) | = | 14 5 |
| 20 | ÷ | 15 | × | ( | 314 5 | − | 477 10 | ) | − | x | ÷ | 15 | × | ( | 314 5 | − | 477 10 | ) | = | 14 5 |
4 3 | ( | 314 5 | − | 477 10 | ) | − | x | × | 1 15 | ( | 314 5 | − | 477 10 | ) | = | 14 5 |
4 3 | × | 314 5 | − | 4 3 | × | 477 10 | − | x | × | 1 15 | ( | 314 5 | − | 477 10 | ) | = | 14 5 |
1256 15 | − | 318 5 | − | x | × | 1 15 | ( | 314 5 | − | 477 10 | ) | = | 14 5 |
302 15 | − | x | × | 1 15 | ( | 314 5 | − | 477 10 | ) | = | 14 5 |
302 15 | − | x | × | 1 15 | × | 314 5 | + | x | × | 1 15 | × | 477 10 | = | 14 5 |
302 15 | − | x | × | 314 75 | + | x | × | 159 50 | = | 14 5 |
302 15 | − | 151 150 | x | = | 14 5 |
Transposition :
| - | 151 150 | x | = | 14 5 | − | 302 15 |
Combine the items on the right of the equation:
| - | 151 150 | x | = | - | 52 3 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
52 3 | = | 151 150 | x |
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 :
151 150 | x | = | 52 3 |
The coefficient of the unknown number is reduced to 1 :
| x | = | 52 3 | ÷ | 151 150 |
| = | 52 3 | × | 150 151 |
| = | 52 | × | 50 151 |
We obtained :
| x | = | 2600 151 |
Convert the result to decimal form :
| x | = | 17.218543 |