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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 4*（x-5） = 20+1.01*（（20-x）-0.5*（x-5）） .
Question type: Equation
Solution:Original question:
| 4 | ( | x | − | 5 | ) | = | 20 | + | 101 100 | ( | ( | 20 | − | x | ) | − | 1 2 | ( | x | − | 5 | ) | ) |
| Left side of the equation = | 4 | x | − | 4 | × | 5 |
| = | 4 | x | − | 20 |
| 4 | x | − | 20 | = | 20 | + | 101 100 | ( | ( | 20 | − | x | ) | − | 1 2 | ( | x | − | 5 | ) | ) |
| Right side of the equation = | 20 | + | 101 100 | ( | 20 | − | x | ) | − | 101 100 | × | 1 2 | ( | x | − | 5 | ) |
| = | 20 | + | 101 100 | ( | 20 | − | x | ) | − | 101 200 | ( | x | − | 5 | ) |
| = | 20 | + | 101 100 | × | 20 | − | 101 100 | x | − | 101 200 | ( | x | − | 5 | ) |
| = | 20 | + | 101 5 | − | 101 100 | x | − | 101 200 | ( | x | − | 5 | ) |
| = | 201 5 | − | 101 100 | x | − | 101 200 | ( | x | − | 5 | ) |
| = | 201 5 | − | 101 100 | x | − | 101 200 | x | + | 101 200 | × | 5 |
| = | 201 5 | − | 101 100 | x | − | 101 200 | x | + | 101 40 |
| = | 1709 40 | − | 303 200 | x |
| 4 | x | − | 20 | = | 1709 40 | − | 303 200 | x |
Transposition :
| 4 | x | + | 303 200 | x | = | 1709 40 | + | 20 |
Combine the items on the left of the equation:
1103 200 | x | = | 1709 40 | + | 20 |
Combine the items on the right of the equation:
1103 200 | x | = | 2509 40 |
The coefficient of the unknown number is reduced to 1 :
| x | = | 2509 40 | ÷ | 1103 200 |
| = | 2509 40 | × | 200 1103 |
| = | 2509 | × | 5 1103 |
We obtained :
| x | = | 12545 1103 |
Convert the result to decimal form :
| x | = | 11.373527 |