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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 (a-290)/410 = (a-515)/210 .
Question type: Equation
Solution:Original question:
| ( | a | − | 290 | ) | ÷ | 410 | = | ( | a | − | 515 | ) | ÷ | 210 |
| Left side of the equation = | a | × | 1 410 | − | 290 | × | 1 410 |
| = | a | × | 1 410 | − | 29 41 |
1 410 | a | − | 29 41 | = | ( | a | − | 515 | ) | ÷ | 210 |
| Right side of the equation = | a | × | 1 210 | − | 515 | × | 1 210 |
| = | a | × | 1 210 | − | 103 42 |
1 410 | a | − | 29 41 | = | 1 210 | a | − | 103 42 |
Transposition :
1 410 | a | − | 1 210 | a | = | - | 103 42 | + | 29 41 |
Combine the items on the left of the equation:
| - | 2 861 | a | = | - | 103 42 | + | 29 41 |
Combine the items on the right of the equation:
| - | 2 861 | a | = | - | 3005 1722 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
3005 1722 | = | 2 861 | a |
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 :
2 861 | a | = | 3005 1722 |
The coefficient of the unknown number is reduced to 1 :
| a | = | 3005 1722 | ÷ | 2 861 |
| = | 3005 1722 | × | 861 2 |
| = | 3005 2 | × | 1 2 |
We obtained :
| a | = | 3005 4 |
Convert the result to decimal form :
| a | = | 751.25 |