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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 （29.73-20）/（30-29.73） = （a-998.2）/（995.7-a） .
Question type: Equation
Solution:Original question:
| ( | 2973 100 | − | 20 | ) | ÷ | ( | 30 | − | 2973 100 | ) | = | ( | a | − | 4991 5 | ) | ÷ | ( | 9957 10 | − | a | ) |
| Multiply both sides of the equation by: | ( | 30 | − | 2973 100 | ) | , | ( | 9957 10 | − | a | ) |
| ( | 2973 100 | − | 20 | ) | ( | 9957 10 | − | a | ) | = | ( | a | − | 4991 5 | ) | ( | 30 | − | 2973 100 | ) |
2973 100 | ( | 9957 10 | − | a | ) | − | 20 | ( | 9957 10 | − | a | ) | = | ( | a | − | 4991 5 | ) | ( | 30 | − | 2973 100 | ) |
2973 100 | ( | 9957 10 | − | a | ) | − | 20 | ( | 9957 10 | − | a | ) | = | a | ( | 30 | − | 2973 100 | ) | − | 4991 5 | ( | 30 | − | 2973 100 | ) |
2973 100 | × | 9957 10 | − | 2973 100 | a | − | 20 | ( | 9957 10 | − | a | ) | = | a | ( | 30 | − | 2973 100 | ) | − | 4991 5 | ( | 30 | − | 2973 100 | ) |
2973 100 | × | 9957 10 | − | 2973 100 | a | − | 20 | ( | 9957 10 | − | a | ) | = | a | × | 30 | − | a | × | 2973 100 | − | 4991 5 | ( | 30 | − | 2973 100 | ) |
29602161 1000 | − | 2973 100 | a | − | 20 | ( | 9957 10 | − | a | ) | = | a | × | 30 | − | a | × | 2973 100 | − | 4991 5 | ( | 30 | − | 2973 100 | ) |
29602161 1000 | − | 2973 100 | a | − | 20 | ( | 9957 10 | − | a | ) | = | 27 100 | a | − | 4991 5 | ( | 30 | − | 2973 100 | ) |
29602161 1000 | − | 2973 100 | a | − | 20 | × | 9957 10 | + | 20 | a | = | 27 100 | a | − | 4991 5 | ( | 30 | − | 2973 100 | ) |
29602161 1000 | − | 2973 100 | a | − | 20 | × | 9957 10 | + | 20 | a | = | 27 100 | a | − | 4991 5 | × | 30 | + | 4991 5 | × | 2973 100 |
29602161 1000 | − | 2973 100 | a | − | 19914 | + | 20 | a | = | 27 100 | a | − | 29946 | + | 14838243 500 |
9688161 1000 | − | 973 100 | a | = | 27 100 | a | − | 134757 500 |
Transposition :
| - | 973 100 | a | − | 27 100 | a | = | - | 134757 500 | − | 9688161 1000 |
Combine the items on the left of the equation:
| - | 10 | a | = | - | 134757 500 | − | 9688161 1000 |
Combine the items on the right of the equation:
| - | 10 | a | = | - | 398307 40 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
398307 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 | = | 398307 40 |
The coefficient of the unknown number is reduced to 1 :
| a | = | 398307 40 | ÷ | 10 |
| = | 398307 40 | × | 1 10 |
We obtained :
| a | = | 398307 400 |
Convert the result to decimal form :
| a | = | 995.7675 |