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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 x = 453+0.16*(4000-x)+0.16{0.16*[4000-x-(453+0.16(4000-x)]} ) .
Question type: Equation
Solution:Original question:
| x | = | 453 | + | 4 25 | ( | 4000 | − | x | ) | + | 4 25 | ( | 4 25 | ( | 4000 | − | x | − | ( | 453 | + | 4 25 | ( | 4000 | − | x | ) | ) | ) | ) |
| Right side of the equation = | 453 | + | 4 25 | × | 4000 | − | 4 25 | x | + | 4 25 | ( | 4 25 | ( | 4000 | − | x | − | ( | 453 | + | 4 25 | ( | 4000 | − | x | ) | ) | ) | ) |
| = | 453 | + | 640 | − | 4 25 | x | + | 4 25 | ( | 4 25 | ( | 4000 | − | x | − | ( | 453 | + | 4 25 | ( | 4000 | − | x | ) | ) | ) | ) |
| = | 1093 | − | 4 25 | x | + | 4 25 | ( | 4 25 | ( | 4000 | − | x | − | ( | 453 | + | 4 25 | ( | 4000 | − | x | ) | ) | ) | ) |
| = | 1093 | − | 4 25 | x | + | 4 25 | × | 4 25 | ( | 4000 | − | x | − | ( | 453 | + | 4 25 | ( | 4000 | − | x | ) | ) | ) |
| = | 1093 | − | 4 25 | x | + | 16 625 | ( | 4000 | − | x | − | ( | 453 | + | 4 25 | ( | 4000 | − | x | ) | ) | ) |
| = | 1093 | − | 4 25 | x | + | 16 625 | × | 4000 | − | 16 625 | x | − | 16 625 | ( | 453 | + | 4 25 | ( | 4000 | − | x | ) | ) |
| = | 1093 | − | 4 25 | x | + | 512 5 | − | 16 625 | x | − | 16 625 | ( | 453 | + | 4 25 | ( | 4000 | − | x | ) | ) |
| = | 5977 5 | − | 116 625 | x | − | 16 625 | ( | 453 | + | 4 25 | ( | 4000 | − | x | ) | ) |
| = | 5977 5 | − | 116 625 | x | − | 16 625 | × | 453 | − | 16 625 | × | 4 25 | ( | 4000 | − | x | ) |
| = | 5977 5 | − | 116 625 | x | − | 7248 625 | − | 64 15625 | ( | 4000 | − | x | ) |
| = | 739877 625 | − | 116 625 | x | − | 64 15625 | ( | 4000 | − | x | ) |
| = | 739877 625 | − | 116 625 | x | − | 64 15625 | × | 4000 | + | 64 15625 | x |
| = | 739877 625 | − | 116 625 | x | − | 2048 125 | + | 64 15625 | x |
| = | 729637 625 | − | 2836 15625 | x |
| x | = | 729637 625 | − | 2836 15625 | x |
Transposition :
| x | + | 2836 15625 | x | = | 729637 625 |
Combine the items on the left of the equation:
18461 15625 | x | = | 729637 625 |
The coefficient of the unknown number is reduced to 1 :
| x | = | 729637 625 | ÷ | 18461 15625 |
| = | 729637 625 | × | 15625 18461 |
| = | 729637 | × | 25 18461 |
We obtained :
| x | = | 18240925 18461 |
Convert the result to decimal form :
| x | = | 988.078923 |