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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 (x+60-277.69)÷(277.69+60) = (x+60-285.5)/285.5 .
Question type: Equation
Solution:Original question:
| ( | x | + | 60 | − | 27769 100 | ) | ÷ | ( | 27769 100 | + | 60 | ) | = | ( | x | + | 60 | − | 571 2 | ) | ÷ | 571 2 |
| Multiply both sides of the equation by: | ( | 27769 100 | + | 60 | ) |
| ( | x | + | 60 | − | 27769 100 | ) | = | ( | x | + | 60 | − | 571 2 | ) | ÷ | 571 2 | × | ( | 27769 100 | + | 60 | ) |
| x | + | 60 | − | 27769 100 | = | ( | x | + | 60 | − | 571 2 | ) | ÷ | 571 2 | × | ( | 27769 100 | + | 60 | ) |
| x | + | 60 | − | 27769 100 | = | x | ÷ | 571 2 | × | ( | 27769 100 | + | 60 | ) | + | 60 | ÷ | 571 2 | × | ( | 27769 100 | + | 60 | ) | − | 571 2 | ÷ | 571 2 | × | ( | 27769 100 | + | 60 | ) |
| x | + | 60 | − | 27769 100 | = | x | × | 2 571 | ( | 27769 100 | + | 60 | ) | + | 120 571 | ( | 27769 100 | + | 60 | ) | − | 1 | ( | 27769 100 | + | 60 | ) |
| x | − | 21769 100 | = | x | × | 2 571 | ( | 27769 100 | + | 60 | ) | + | 120 571 | ( | 27769 100 | + | 60 | ) | − | 1 | ( | 27769 100 | + | 60 | ) |
| x | − | 21769 100 | = | x | × | 2 571 | × | 27769 100 | + | x | × | 2 571 | × | 60 | + | 120 571 | ( | 27769 100 | + | 60 | ) | − | 1 | ( | 27769 100 | + | 60 | ) |
| x | − | 21769 100 | = | x | × | 27769 28550 | + | x | × | 120 571 | + | 120 571 | ( | 27769 100 | + | 60 | ) | − | 1 | ( | 27769 100 | + | 60 | ) |
| x | − | 21769 100 | = | 33769 28550 | x | + | 120 571 | ( | 27769 100 | + | 60 | ) | − | 1 | ( | 27769 100 | + | 60 | ) |
| x | − | 21769 100 | = | 33769 28550 | x | + | 120 571 | × | 27769 100 | + | 120 571 | × | 60 | − | 1 | ( | 27769 100 | + | 60 | ) |
| x | − | 21769 100 | = | 33769 28550 | x | + | 166614 2855 | + | 7200 571 | − | 1 | ( | 27769 100 | + | 60 | ) |
| x | − | 21769 100 | = | 33769 28550 | x | + | 202614 2855 | − | 1 | ( | 27769 100 | + | 60 | ) |
| x | − | 21769 100 | = | 33769 28550 | x | + | 202614 2855 | − | 1 | × | 27769 100 | − | 1 | × | 60 |
| x | − | 21769 100 | = | 33769 28550 | x | + | 202614 2855 | − | 27769 100 | − | 60 |
| x | − | 21769 100 | = | 33769 28550 | x | − | 15229819 57100 |
Transposition :
| x | − | 33769 28550 | x | = | - | 15229819 57100 | + | 21769 100 |
Combine the items on the left of the equation:
| - | 5219 28550 | x | = | - | 15229819 57100 | + | 21769 100 |
Combine the items on the right of the equation:
| - | 5219 28550 | x | = | - | 139986 2855 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
139986 2855 | = | 5219 28550 | 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 :
5219 28550 | x | = | 139986 2855 |
The coefficient of the unknown number is reduced to 1 :
| x | = | 139986 2855 | ÷ | 5219 28550 |
| = | 139986 2855 | × | 28550 5219 |
| = | 139986 571 | × | 5710 5219 |
We obtained :
| x | = | 799320060 2980049 |
By reducing fraction, we can get:
| x | = | 1399860 5219 |
Convert the result to decimal form :
| x | = | 268.223798 |