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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 = 25.8/(85.8-52.9) .
Question type: Equation
Solution:Original question:
| ( | 20 | − | x | ) | ÷ | 15 | = | 129 5 | ÷ | ( | 429 5 | − | 529 10 | ) |
| Multiply both sides of the equation by: | ( | 429 5 | − | 529 10 | ) |
| ( | 20 | − | x | ) | ÷ | 15 | × | ( | 429 5 | − | 529 10 | ) | = | 129 5 |
| 20 | ÷ | 15 | × | ( | 429 5 | − | 529 10 | ) | − | x | ÷ | 15 | × | ( | 429 5 | − | 529 10 | ) | = | 129 5 |
4 3 | ( | 429 5 | − | 529 10 | ) | − | x | × | 1 15 | ( | 429 5 | − | 529 10 | ) | = | 129 5 |
4 3 | × | 429 5 | − | 4 3 | × | 529 10 | − | x | × | 1 15 | ( | 429 5 | − | 529 10 | ) | = | 129 5 |
572 5 | − | 1058 15 | − | x | × | 1 15 | ( | 429 5 | − | 529 10 | ) | = | 129 5 |
658 15 | − | x | × | 1 15 | ( | 429 5 | − | 529 10 | ) | = | 129 5 |
658 15 | − | x | × | 1 15 | × | 429 5 | + | x | × | 1 15 | × | 529 10 | = | 129 5 |
658 15 | − | x | × | 143 25 | + | x | × | 529 150 | = | 129 5 |
658 15 | − | 329 150 | x | = | 129 5 |
Transposition :
| - | 329 150 | x | = | 129 5 | − | 658 15 |
Combine the items on the right of the equation:
| - | 329 150 | x | = | - | 271 15 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
271 15 | = | 329 150 | 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 :
329 150 | x | = | 271 15 |
The coefficient of the unknown number is reduced to 1 :
| x | = | 271 15 | ÷ | 329 150 |
| = | 271 15 | × | 150 329 |
| = | 271 | × | 10 329 |
We obtained :
| x | = | 2710 329 |
Convert the result to decimal form :
| x | = | 8.237082 |