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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 （0.994-0.769）*100+（0.994-x）*200+（0.818-0.790）*300+（0.819-0.790）*300+0.1+0.1+0.2+0.2 = （0.994-0.769）*300+0.1 .
Question type: Equation
Solution:Original question:
| ( | 497 500 | − | 769 1000 | ) | × | 100 | + | ( | 497 500 | − | x | ) | × | 200 | + | ( | 409 500 | − | 79 100 | ) | × | 300 | + | ( | 819 1000 | − | 79 100 | ) | × | 300 | + | 1 10 | + | 1 10 | + | 1 5 | + | 1 5 | = | ( | 497 500 | − | 769 1000 | ) | × | 300 | + | 1 10 |
| Left side of the equation = | ( | 497 500 | − | 769 1000 | ) | × | 100 | + | ( | 497 500 | − | x | ) | × | 200 | + | ( | 409 500 | − | 79 100 | ) | × | 300 | + | ( | 819 1000 | − | 79 100 | ) | × | 300 | + | 3 5 |
| ( | 497 500 | − | 769 1000 | ) | × | 100 | + | ( | 497 500 | − | x | ) | × | 200 | + | ( | 409 500 | − | 79 100 | ) | × | 300 | + | ( | 819 1000 | − | 79 100 | ) | × | 300 | + | 3 5 | = | ( | 497 500 | − | 769 1000 | ) | × | 300 | + | 1 10 |
| Left side of the equation = | 497 500 | × | 100 | − | 769 1000 | × | 100 | + | ( | 497 500 | − | x | ) | × | 200 | + | ( | 409 500 | − | 79 100 | ) | × | 300 | + | ( | 819 1000 | − | 79 100 | ) | × | 300 | + | 3 5 |
| = | 497 5 | − | 769 10 | + | ( | 497 500 | − | x | ) | × | 200 | + | ( | 409 500 | − | 79 100 | ) | × | 300 | + | ( | 819 1000 | − | 79 100 | ) | × | 300 | + | 3 5 |
| = | 231 10 | + | ( | 497 500 | − | x | ) | × | 200 | + | ( | 409 500 | − | 79 100 | ) | × | 300 | + | ( | 819 1000 | − | 79 100 | ) | × | 300 |
| = | 231 10 | + | 497 500 | × | 200 | − | x | × | 200 | + | ( | 409 500 | − | 79 100 | ) | × | 300 | + | ( | 819 1000 | − | 79 100 | ) | × | 300 |
| = | 231 10 | + | 994 5 | − | x | × | 200 | + | ( | 409 500 | − | 79 100 | ) | × | 300 | + | ( | 819 1000 | − | 79 100 | ) | × | 300 |
| = | 2219 10 | − | 200 | x | + | ( | 409 500 | − | 79 100 | ) | × | 300 | + | ( | 819 1000 | − | 79 100 | ) | × | 300 |
| = | 2219 10 | − | 200 | x | + | 409 500 | × | 300 | − | 79 100 | × | 300 | + | ( | 819 1000 | − | 79 100 | ) | × | 300 |
| = | 2219 10 | − | 200 | x | + | 1227 5 | − | 237 | + | ( | 819 1000 | − | 79 100 | ) | × | 300 |
| = | 2303 10 | − | 200 | x | + | ( | 819 1000 | − | 79 100 | ) | × | 300 |
| = | 2303 10 | − | 200 | x | + | 819 1000 | × | 300 | − | 79 100 | × | 300 |
| = | 2303 10 | − | 200 | x | + | 2457 10 | − | 237 |
| = | 239 | − | 200 | x |
| 239 | − | 200 | x | = | ( | 497 500 | − | 769 1000 | ) | × | 300 | + | 1 10 |
| Right side of the equation = | 497 500 | × | 300 | − | 769 1000 | × | 300 | + | 1 10 |
| = | 1491 5 | − | 2307 10 | + | 1 10 |
| = | 338 5 |
| 239 | − | 200 | x | = | 338 5 |
Transposition :
| - | 200 | x | = | 338 5 | − | 239 |
Combine the items on the right of the equation:
| - | 200 | x | = | - | 857 5 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
857 5 | = | 200 | 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 :
| 200 | x | = | 857 5 |
The coefficient of the unknown number is reduced to 1 :
| x | = | 857 5 | ÷ | 200 |
| = | 857 5 | × | 1 200 |
We obtained :
| x | = | 857 1000 |
Convert the result to decimal form :
| x | = | 0.857 |