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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 (30-100*x)*0.6*(1+4.2*x)-(4.56-7.6*x)*(1+4.2x) = 5.2*x*(30-100*x) .
Question type: Equation
Solution:Original question:
| ( | 30 | − | 100 | x | ) | × | 3 5 | ( | 1 | + | 21 5 | x | ) | − | ( | 114 25 | − | 38 5 | x | ) | ( | 1 | + | 21 5 | x | ) | = | 26 5 | x | ( | 30 | − | 100 | x | ) |
| Left side of the equation = | 30 | × | 3 5 | ( | 1 | + | 21 5 | x | ) | − | 100 | x | × | 3 5 | ( | 1 | + | 21 5 | x | ) | − | ( | 114 25 | − | 38 5 | x | ) | ( | 1 | + | 21 5 | x | ) |
| = | 18 | ( | 1 | + | 21 5 | x | ) | − | 60 | x | ( | 1 | + | 21 5 | x | ) | − | ( | 114 25 | − | 38 5 | x | ) | ( | 1 | + | 21 5 | x | ) |
| = | 18 | × | 1 | + | 18 | × | 21 5 | x | − | 60 | x | ( | 1 | + | 21 5 | x | ) | − | ( | 114 25 | − | 38 5 | x | ) | ( | 1 | + | 21 5 | x | ) |
| = | 18 | + | 378 5 | x | − | 60 | x | ( | 1 | + | 21 5 | x | ) | − | ( | 114 25 | − | 38 5 | x | ) | ( | 1 | + | 21 5 | x | ) |
| = | 18 | + | 378 5 | x | − | 60 | x | × | 1 | − | 60 | x | × | 21 5 | x | − | ( | 114 25 | − | 38 5 | x | ) | ( | 1 | + | 21 5 | x | ) |
| = | 18 | + | 378 5 | x | − | 60 | x | − | 252 | x | x | − | ( | 114 25 | − | 38 5 | x | ) | ( | 1 | + | 21 5 | x | ) |
| = | 18 | + | 78 5 | x | − | 252 | x | x | − | ( | 114 25 | − | 38 5 | x | ) | ( | 1 | + | 21 5 | x | ) |
| = | 18 | + | 78 5 | x | − | 252 | x | x | − | 114 25 | ( | 1 | + | 21 5 | x | ) | + | 38 5 | x | ( | 1 | + | 21 5 | x | ) |
| = | 18 | + | 78 5 | x | − | 252 | x | x | − | 114 25 | × | 1 | − | 114 25 | × | 21 5 | x | + | 38 5 |
| = | 18 | + | 78 5 | x | − | 252 | x | x | − | 114 25 | − | 2394 125 | x | + | 38 5 | x | ( | 1 | + | 21 5 | x | ) |
| = | 336 25 | − | 444 125 | x | − | 252 | x | x | + | 38 5 | x | ( | 1 | + | 21 5 | x | ) |
| = | 336 25 | − | 444 125 | x | − | 252 | x | x | + | 38 5 | x | × | 1 | + | 38 5 | x | × | 21 5 |
| = | 336 25 | − | 444 125 | x | − | 252 | x | x | + | 38 5 | x | + | 798 25 | x | x |
| = | 336 25 | + | 506 125 | x | − | 252 | x | x | + | 798 25 | x | x |
336 25 | + | 506 125 | x | − | 252 | x | x | + | 798 25 | x | x | = | 26 5 | x | ( | 30 | − | 100 | x | ) |
| Right side of the equation = | 26 5 | x | × | 30 | − | 26 5 | x | × | 100 | x |
| = | 156 | x | − | 520 | x | x |
336 25 | + | 506 125 | x | − | 252 | x | x | + | 798 25 | x | x | = | 156 | x | − | 520 | x | x |
The solution of the equation:
x1≈0.114182 , keep 6 decimal places
x2≈0.392459 , keep 6 decimal places
There are 2 solution(s).
解程的详细方法请参阅：《方程的解法》