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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 （28.51-20）/（30-28.51） = （a-998.2）/（995.7-a） .
Question type: Equation
Solution:Original question:
| ( | 2851 100 | − | 20 | ) | ÷ | ( | 30 | − | 2851 100 | ) | = | ( | a | − | 4991 5 | ) | ÷ | ( | 9957 10 | − | a | ) |
| Multiply both sides of the equation by: | ( | 30 | − | 2851 100 | ) | , | ( | 9957 10 | − | a | ) |
| ( | 2851 100 | − | 20 | ) | ( | 9957 10 | − | a | ) | = | ( | a | − | 4991 5 | ) | ( | 30 | − | 2851 100 | ) |
2851 100 | ( | 9957 10 | − | a | ) | − | 20 | ( | 9957 10 | − | a | ) | = | ( | a | − | 4991 5 | ) | ( | 30 | − | 2851 100 | ) |
2851 100 | ( | 9957 10 | − | a | ) | − | 20 | ( | 9957 10 | − | a | ) | = | a | ( | 30 | − | 2851 100 | ) | − | 4991 5 | ( | 30 | − | 2851 100 | ) |
2851 100 | × | 9957 10 | − | 2851 100 | a | − | 20 | ( | 9957 10 | − | a | ) | = | a | ( | 30 | − | 2851 100 | ) | − | 4991 5 | ( | 30 | − | 2851 100 | ) |
2851 100 | × | 9957 10 | − | 2851 100 | a | − | 20 | ( | 9957 10 | − | a | ) | = | a | × | 30 | − | a | × | 2851 100 | − | 4991 5 | ( | 30 | − | 2851 100 | ) |
28387407 1000 | − | 2851 100 | a | − | 20 | ( | 9957 10 | − | a | ) | = | a | × | 30 | − | a | × | 2851 100 | − | 4991 5 | ( | 30 | − | 2851 100 | ) |
28387407 1000 | − | 2851 100 | a | − | 20 | ( | 9957 10 | − | a | ) | = | 149 100 | a | − | 4991 5 | ( | 30 | − | 2851 100 | ) |
28387407 1000 | − | 2851 100 | a | − | 20 | × | 9957 10 | + | 20 | a | = | 149 100 | a | − | 4991 5 | ( | 30 | − | 2851 100 | ) |
28387407 1000 | − | 2851 100 | a | − | 20 | × | 9957 10 | + | 20 | a | = | 149 100 | a | − | 4991 5 | × | 30 | + | 4991 5 | × | 2851 100 |
28387407 1000 | − | 2851 100 | a | − | 19914 | + | 20 | a | = | 149 100 | a | − | 29946 | + | 14229341 500 |
8473407 1000 | − | 851 100 | a | = | 149 100 | a | − | 743659 500 |
Transposition :
| - | 851 100 | a | − | 149 100 | a | = | - | 743659 500 | − | 8473407 1000 |
Combine the items on the left of the equation:
| - | 10 | a | = | - | 743659 500 | − | 8473407 1000 |
Combine the items on the right of the equation:
| - | 10 | a | = | - | 398429 40 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
398429 40 | = | 10 | 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 :
| 10 | a | = | 398429 40 |
The coefficient of the unknown number is reduced to 1 :
| a | = | 398429 40 | ÷ | 10 |
| = | 398429 40 | × | 1 10 |
We obtained :
| a | = | 398429 400 |
Convert the result to decimal form :
| a | = | 996.0725 |