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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 {0.5[x-0.5(x-1)]}:(0.75x) = 0.114514 .
Question type: Equation
Solution:Original question:
| ( | 1 2 | ( | x | − | 1 2 | ( | x | − | 1 | ) | ) | ) | ÷ | ( | 3 4 | x | ) | = | 57257 500000 |
| Multiply both sides of the equation by: | ( | 3 4 | x | ) |
| ( | 1 2 | ( | x | − | 1 2 | ( | x | − | 1 | ) | ) | ) | = | 57257 500000 | ( | 3 4 | x | ) |
1 2 | ( | x | − | 1 2 | ( | x | − | 1 | ) | ) | = | 57257 500000 | ( | 3 4 | x | ) |
1 2 | ( | x | − | 1 2 | ( | x | − | 1 | ) | ) | = | 57257 500000 | × | 3 4 | x |
1 2 | ( | x | − | 1 2 | ( | x | − | 1 | ) | ) | = | 171771 2000000 | x |
1 2 | x | − | 1 2 | × | 1 2 | ( | x | − | 1 | ) | = | 171771 2000000 | x |
1 2 | x | − | 1 4 | ( | x | − | 1 | ) | = | 171771 2000000 | x |
1 2 | x | − | 1 4 | x | + | 1 4 | × | 1 | = | 171771 2000000 | x |
1 2 | x | − | 1 4 | x | + | 1 4 | = | 171771 2000000 | x |
1 4 | x | + | 1 4 | = | 171771 2000000 | x |
Transposition :
1 4 | x | − | 171771 2000000 | x | = | - | 1 4 |
Combine the items on the left of the equation:
328229 2000000 | x | = | - | 1 4 |
The coefficient of the unknown number is reduced to 1 :
| x | = | - | 1 4 | ÷ | 328229 2000000 |
| = | - | 1 4 | × | 2000000 328229 |
| = | - | 1 | × | 500000 328229 |
We obtained :
| x | = | - | 500000 328229 |
Convert the result to decimal form :
| x | = | - 1.523327 |