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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 299.7(10.1010-r) = （r+1000）*0.3 .
Question type: Equation
Solution:Original question:
2997 10 | ( | 10101 1000 | − | r | ) | = | ( | r | + | 1000 | ) | × | 3 10 |
| Left side of the equation = | 2997 10 | × | 10101 1000 | − | 2997 10 | r |
| = | 30272697 10000 | − | 2997 10 | r |
30272697 10000 | − | 2997 10 | r | = | ( | r | + | 1000 | ) | × | 3 10 |
| Right side of the equation = | r | × | 3 10 | + | 1000 | × | 3 10 |
| = | r | × | 3 10 | + | 300 |
30272697 10000 | − | 2997 10 | r | = | 3 10 | r | + | 300 |
Transposition :
| - | 2997 10 | r | − | 3 10 | r | = | 300 | − | 30272697 10000 |
Combine the items on the left of the equation:
| - | 300 | r | = | 300 | − | 30272697 10000 |
Combine the items on the right of the equation:
| - | 300 | r | = | - | 27272697 10000 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
27272697 10000 | = | 300 | r |
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 :
| 300 | r | = | 27272697 10000 |
The coefficient of the unknown number is reduced to 1 :
| r | = | 27272697 10000 | ÷ | 300 |
| = | 27272697 10000 | × | 1 300 |
| = | 9090899 10000 | × | 1 100 |
We obtained :
| r | = | 9090899 1000000 |
Convert the result to decimal form :
| r | = | 9.090899 |