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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
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Work: Find the solution of equation 10/(36+0.966+0.483+0.450+0.45+x) = 2.5/(10-0.966-0.483-0.45-0.450-x) .
Question type: Equation
Solution:Original question:
| 10 | ÷ | ( | 36 | + | 483 500 | + | 483 1000 | + | 9 20 | + | 9 20 | + | x | ) | = | 5 2 | ÷ | ( | 10 | − | 483 500 | − | 483 1000 | − | 9 20 | − | 9 20 | − | x | ) |
| Multiply both sides of the equation by: | ( | 36 | + | 483 500 | + | 483 1000 | + | 9 20 | + | 9 20 | + | x | ) | , | ( | 10 | − | 483 500 | − | 483 1000 | − | 9 20 | − | 9 20 | − | x | ) |
| 10 | ( | 10 | − | 483 500 | − | 483 1000 | − | 9 20 | − | 9 20 | − | x | ) | = | 5 2 | ( | 36 | + | 483 500 | + | 483 1000 | + | 9 20 | + | 9 20 | + | x | ) |
| 10 | × | 10 | − | 10 | × | 483 500 | − | 10 | × | 483 1000 | − | 10 | × | 9 20 | − | 10 | × | 9 20 | − | 10 | x | = | 5 2 | ( | 36 | + | 483 500 | + | 483 1000 | + | 9 20 | + | 9 20 | + | x | ) |
| 10 | × | 10 | − | 10 | × | 483 500 | − | 10 | × | 483 1000 | − | 10 | × | 9 20 | − | 10 | × | 9 20 | − | 10 | x | = | 5 2 | × | 36 | + | 5 2 | × | 483 500 | + | 5 2 | × | 483 1000 | + | 5 2 | × | 9 20 | + | 5 2 | × | 9 20 | + | 5 2 | x |
| 100 | − | 483 50 | − | 483 100 | − | 9 2 | − | 9 2 | − | 10 | x | = | 90 | + | 483 200 | + | 483 400 | + | 9 8 | + | 9 8 | + | 5 2 | x |
7651 100 | − | 10 | x | = | 38349 400 | + | 5 2 | x |
Transposition :
| - | 10 | x | − | 5 2 | x | = | 38349 400 | − | 7651 100 |
Combine the items on the left of the equation:
| - | 25 2 | x | = | 38349 400 | − | 7651 100 |
Combine the items on the right of the equation:
| - | 25 2 | x | = | 1549 80 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
| - | 1549 80 | = | 25 2 | 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 :
25 2 | x | = | - | 1549 80 |
The coefficient of the unknown number is reduced to 1 :
| x | = | - | 1549 80 | ÷ | 25 2 |
| = | - | 1549 80 | × | 2 25 |
| = | - | 1549 40 | × | 1 25 |
We obtained :
| x | = | - | 1549 1000 |
Convert the result to decimal form :
| x | = | - 1.549 |