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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 = 30.7/(90.7-56.8) .
Question type: Equation
Solution:Original question:
| ( | 20 | − | x | ) | ÷ | 15 | = | 307 10 | ÷ | ( | 907 10 | − | 284 5 | ) |
| Multiply both sides of the equation by: | ( | 907 10 | − | 284 5 | ) |
| ( | 20 | − | x | ) | ÷ | 15 | × | ( | 907 10 | − | 284 5 | ) | = | 307 10 |
| 20 | ÷ | 15 | × | ( | 907 10 | − | 284 5 | ) | − | x | ÷ | 15 | × | ( | 907 10 | − | 284 5 | ) | = | 307 10 |
4 3 | ( | 907 10 | − | 284 5 | ) | − | x | × | 1 15 | ( | 907 10 | − | 284 5 | ) | = | 307 10 |
4 3 | × | 907 10 | − | 4 3 | × | 284 5 | − | x | × | 1 15 | ( | 907 10 | − | 284 5 | ) | = | 307 10 |
1814 15 | − | 1136 15 | − | x | × | 1 15 | ( | 907 10 | − | 284 5 | ) | = | 307 10 |
226 5 | − | x | × | 1 15 | ( | 907 10 | − | 284 5 | ) | = | 307 10 |
226 5 | − | x | × | 1 15 | × | 907 10 | + | x | × | 1 15 | × | 284 5 | = | 307 10 |
226 5 | − | x | × | 907 150 | + | x | × | 284 75 | = | 307 10 |
226 5 | − | 113 50 | x | = | 307 10 |
Transposition :
| - | 113 50 | x | = | 307 10 | − | 226 5 |
Combine the items on the right of the equation:
| - | 113 50 | x | = | - | 29 2 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
29 2 | = | 113 50 | 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 :
113 50 | x | = | 29 2 |
The coefficient of the unknown number is reduced to 1 :
| x | = | 29 2 | ÷ | 113 50 |
| = | 29 2 | × | 50 113 |
| = | 29 | × | 25 113 |
We obtained :
| x | = | 725 113 |
Convert the result to decimal form :
| x | = | 6.415929 |