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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 0.507/0.493 = (40/x+8.5)/(50/x+6.8) .
Question type: Equation
Solution:Original question:
507 1000 | ÷ | 493 1000 | = | ( | 40 | ÷ | x | + | 17 2 | ) | ÷ | ( | 50 | ÷ | x | + | 34 5 | ) |
| Multiply both sides of the equation by: | ( | 50 | ÷ | x | + | 34 5 | ) |
507 1000 | ÷ | 493 1000 | × | ( | 50 | ÷ | x | + | 34 5 | ) | = | ( | 40 | ÷ | x | + | 17 2 | ) |
507 1000 | ÷ | 493 1000 | × | 50 | ÷ | x | + | 507 1000 | ÷ | 493 1000 | × | 34 5 | = | ( | 40 | ÷ | x | + | 17 2 | ) |
507 1000 | ÷ | 493 1000 | × | 50 | ÷ | x | + | 507 1000 | ÷ | 493 1000 | × | 34 5 | = | 40 | ÷ | x | + | 17 2 |
25350 493 | ÷ | x | + | 1014 145 | = | 40 | ÷ | x | + | 17 2 |
| Multiply both sides of the equation by: | x |
25350 493 | + | 1014 145 | x | = | 40 | ÷ | 1 | × | 1 | + | 17 2 | x |
Transposition :
1014 145 | x | − | 17 2 | x | = | 40 | ÷ | 1 | × | 1 | − | 25350 493 |
Calculate the items on the right of the equation:
1014 145 | x | − | 17 2 | x | = | 40 | − | 25350 493 |
Combine the items on the left of the equation:
| - | 437 290 | x | = | 40 | − | 25350 493 |
Combine the items on the right of the equation:
| - | 437 290 | x | = | - | 5630 493 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
5630 493 | = | 437 290 | 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 :
437 290 | x | = | 5630 493 |
The coefficient of the unknown number is reduced to 1 :
| x | = | 5630 493 | ÷ | 437 290 |
| = | 5630 493 | × | 290 437 |
We obtained :
| x | = | 1632700 215441 |
By reducing fraction, we can get:
| x | = | 56300 7429 |
Convert the result to decimal form :
| x | = | 7.578409 |