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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 168/342/（1.68/342+20/18+n） = 245/690/（2.45/690+20/18-n ) .
Question type: Equation
Solution:Original question:
| 168 | ÷ | 342 | ÷ | ( | 42 25 | ÷ | 342 | + | 20 | ÷ | 18 | + | n | ) | = | 245 | ÷ | 690 | ÷ | ( | 49 20 | ÷ | 690 | + | 20 | ÷ | 18 | − | n | ) |
| Multiply both sides of the equation by: | ( | 42 25 | ÷ | 342 | + | 20 | ÷ | 18 | + | n | ) | , | ( | 49 20 | ÷ | 690 | + | 20 | ÷ | 18 | − | n | ) |
| 168 | ÷ | 342 | × | ( | 49 20 | ÷ | 690 | + | 20 | ÷ | 18 | − | n | ) | = | 245 | ÷ | 690 | × | ( | 42 25 | ÷ | 342 | + | 20 | ÷ | 18 | + | n | ) |
| 168 | ÷ | 342 | × | 49 20 | ÷ | 690 | + | 168 | ÷ | 342 | × | 20 | ÷ | 18 | − | 168 | ÷ | 342 | × | n | = | 245 | ÷ | 690 | × | ( | 42 25 | ÷ | 342 | + | 20 | ÷ | 18 | + | n | ) |
| 168 | ÷ | 342 | × | 49 20 | ÷ | 690 | + | 168 | ÷ | 342 | × | 20 | ÷ | 18 | − | 168 | ÷ | 342 | × | n | = | 245 | ÷ | 690 | × | 42 25 | ÷ | 342 | + | 245 | ÷ | 690 | × | 20 | ÷ | 18 | + | 245 | ÷ | 690 | × | n |
343 196650 | + | 280 513 | − | 28 57 | n | = | 343 196650 | + | 245 621 | + | 49 138 | n |
323029 589950 | − | 28 57 | n | = | 233779 589950 | + | 49 138 | n |
Transposition :
| - | 28 57 | n | − | 49 138 | n | = | 233779 589950 | − | 323029 589950 |
Combine the items on the left of the equation:
| - | 2219 2622 | n | = | 233779 589950 | − | 323029 589950 |
Combine the items on the right of the equation:
| - | 2219 2622 | n | = | - | 595 3933 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
595 3933 | = | 2219 2622 | n |
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 :
2219 2622 | n | = | 595 3933 |
The coefficient of the unknown number is reduced to 1 :
| n | = | 595 3933 | ÷ | 2219 2622 |
| = | 595 3933 | × | 2622 2219 |
| = | 85 3 | × | 2 317 |
We obtained :
| n | = | 170 951 |
Convert the result to decimal form :
| n | = | 0.178759 |