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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 (1.165-x)*(40-31.4) = (x-1.128)*1.4 .
Question type: Equation
Solution:Original question:
| ( | 233 200 | − | x | ) | ( | 40 | − | 157 5 | ) | = | ( | x | − | 141 125 | ) | × | 7 5 |
| Left side of the equation = | 233 200 | ( | 40 | − | 157 5 | ) | − | x | ( | 40 | − | 157 5 | ) |
| = | 233 200 | × | 40 | − | 233 200 | × | 157 5 | − | x | ( | 40 | − | 157 5 | ) |
| = | 233 5 | − | 36581 1000 | − | x | ( | 40 | − | 157 5 | ) |
| = | 10019 1000 | − | x | ( | 40 | − | 157 5 | ) |
| = | 10019 1000 | − | x | × | 40 | + | x | × | 157 5 |
| = | 10019 1000 | − | 43 5 | x |
10019 1000 | − | 43 5 | x | = | ( | x | − | 141 125 | ) | × | 7 5 |
| Right side of the equation = | x | × | 7 5 | − | 141 125 | × | 7 5 |
| = | x | × | 7 5 | − | 987 625 |
10019 1000 | − | 43 5 | x | = | 7 5 | x | − | 987 625 |
Transposition :
| - | 43 5 | x | − | 7 5 | x | = | - | 987 625 | − | 10019 1000 |
Combine the items on the left of the equation:
| - | 10 | x | = | - | 987 625 | − | 10019 1000 |
Combine the items on the right of the equation:
| - | 10 | x | = | - | 57991 5000 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
57991 5000 | = | 10 | 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 :
| 10 | x | = | 57991 5000 |
The coefficient of the unknown number is reduced to 1 :
| x | = | 57991 5000 | ÷ | 10 |
| = | 57991 5000 | × | 1 10 |
We obtained :
| x | = | 57991 50000 |
Convert the result to decimal form :
| x | = | 1.15982 |