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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/1.03*0.03+(1-X)/1.13*0.13 = 1/1.09*0.09 .
Question type: Equation
Solution:Original question:
The equation is transformed into :
Remove the bracket on the left of the equation:
The equation is transformed into :
The equation is transformed into :
Transposition :
Combine the items on the right of the equation:
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
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 :
The coefficient of the unknown number is reduced to 1 :
We obtained :
This is the solution of the equation.
By reducing fraction, we can get:
Convert the result to decimal form :
☆1 equations
[ 1/1 Equation]
Work: Find the solution of equation X/1.03*0.03+(1-X)/1.13*0.13 = 1/1.09*0.09 .
Question type: Equation
Solution:Original question:
| X | ÷ | 103 100 | × | 3 100 | + | ( | 1 | − | X | ) | ÷ | 113 100 | × | 13 100 | = | 1 | ÷ | 109 100 | × | 9 100 |
| Left side of the equation = | X | × | 3 103 | + | ( | 1 | − | X | ) | × | 13 113 |
3 103 | X | + | ( | 1 | − | X | ) | × | 13 113 | = | 1 | ÷ | 109 100 | × | 9 100 |
| Left side of the equation = | 3 103 | X | + | 1 | × | 13 113 | − | X | × | 13 113 |
| = | 3 103 | X | + | 13 113 | − | X | × | 13 113 |
| = | - | 1000 11639 | X | + | 13 113 |
| - | 1000 11639 | X | + | 13 113 | = | 1 | ÷ | 109 100 | × | 9 100 |
| Right side of the equation = | 9 109 |
| - | 1000 11639 | X | + | 13 113 | = | 9 109 |
Transposition :
| - | 1000 11639 | X | = | 9 109 | − | 13 113 |
Combine the items on the right of the equation:
| - | 1000 11639 | X | = | - | 400 12317 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
400 12317 | = | 1000 11639 | 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 :
1000 11639 | X | = | 400 12317 |
The coefficient of the unknown number is reduced to 1 :
| X | = | 400 12317 | ÷ | 1000 11639 |
| = | 400 12317 | × | 11639 1000 |
| = | 2 12317 | × | 11639 5 |
We obtained :
| X | = | 23278 61585 |
By reducing fraction, we can get:
| X | = | 206 545 |
Convert the result to decimal form :
| X | = | 0.377982 |