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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+60-277.5)÷(277.5+60) = (x+60-285)/285 .
Question type: Equation
Solution:Original question:
| ( | x | + | 60 | − | 555 2 | ) | ÷ | ( | 555 2 | + | 60 | ) | = | ( | x | + | 60 | − | 285 | ) | ÷ | 285 |
| Multiply both sides of the equation by: | ( | 555 2 | + | 60 | ) |
| ( | x | + | 60 | − | 555 2 | ) | = | ( | x | + | 60 | − | 285 | ) | ÷ | 285 | × | ( | 555 2 | + | 60 | ) |
| x | + | 60 | − | 555 2 | = | ( | x | + | 60 | − | 285 | ) | ÷ | 285 | × | ( | 555 2 | + | 60 | ) |
| x | + | 60 | − | 555 2 | = | x | ÷ | 285 | × | ( | 555 2 | + | 60 | ) | + | 60 | ÷ | 285 | × | ( | 555 2 | + | 60 | ) | − | 285 | ÷ | 285 | × | ( | 555 2 | + | 60 | ) |
| x | + | 60 | − | 555 2 | = | x | × | 1 285 | ( | 555 2 | + | 60 | ) | + | 4 19 | ( | 555 2 | + | 60 | ) | − | 1 | ( | 555 2 | + | 60 | ) |
| x | − | 435 2 | = | x | × | 1 285 | ( | 555 2 | + | 60 | ) | + | 4 19 | ( | 555 2 | + | 60 | ) | − | 1 | ( | 555 2 | + | 60 | ) |
| x | − | 435 2 | = | x | × | 1 285 | × | 555 2 | + | x | × | 1 285 | × | 60 | + | 4 19 | ( | 555 2 | + | 60 | ) | − | 1 | ( | 555 2 | + | 60 | ) |
| x | − | 435 2 | = | x | × | 37 38 | + | x | × | 4 19 | + | 4 19 | ( | 555 2 | + | 60 | ) | − | 1 | ( | 555 2 | + | 60 | ) |
| x | − | 435 2 | = | 45 38 | x | + | 4 19 | ( | 555 2 | + | 60 | ) | − | 1 | ( | 555 2 | + | 60 | ) |
| x | − | 435 2 | = | 45 38 | x | + | 4 19 | × | 555 2 | + | 4 19 | × | 60 | − | 1 | ( | 555 2 | + | 60 | ) |
| x | − | 435 2 | = | 45 38 | x | + | 1110 19 | + | 240 19 | − | 1 | ( | 555 2 | + | 60 | ) |
| x | − | 435 2 | = | 45 38 | x | + | 1350 19 | − | 1 | ( | 555 2 | + | 60 | ) |
| x | − | 435 2 | = | 45 38 | x | + | 1350 19 | − | 1 | × | 555 2 | − | 1 | × | 60 |
| x | − | 435 2 | = | 45 38 | x | + | 1350 19 | − | 555 2 | − | 60 |
| x | − | 435 2 | = | 45 38 | x | − | 10125 38 |
Transposition :
| x | − | 45 38 | x | = | - | 10125 38 | + | 435 2 |
Combine the items on the left of the equation:
| - | 7 38 | x | = | - | 10125 38 | + | 435 2 |
Combine the items on the right of the equation:
| - | 7 38 | x | = | - | 930 19 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
930 19 | = | 7 38 | 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 :
7 38 | x | = | 930 19 |
The coefficient of the unknown number is reduced to 1 :
| x | = | 930 19 | ÷ | 7 38 |
| = | 930 19 | × | 38 7 |
| = | 930 | × | 2 7 |
We obtained :
| x | = | 1860 7 |
Convert the result to decimal form :
| x | = | 265.714286 |