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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 (0.75-x)(80/41-x)-(0.5+x)(80/41-x)-(0.75-x)(0.5+x) = 0 .
Question type: Equation
Solution:Original question:
Remove the bracket on the left of the equation:
The equation is transformed into :
The solution of the equation:
x1≈0.026087 , keep 6 decimal places
x2≈1.441393 , keep 6 decimal places
There are 2 solution(s).
解程的详细方法请参阅：《方程的解法》
☆1 equations
[ 1/1 Equation]
Work: Find the solution of equation (0.75-x)(80/41-x)-(0.5+x)(80/41-x)-(0.75-x)(0.5+x) = 0 .
Question type: Equation
Solution:Original question:
| ( | 3 4 | − | x | ) | ( | 80 | ÷ | 41 | − | x | ) | − | ( | 1 2 | + | x | ) | ( | 80 | ÷ | 41 | − | x | ) | − | ( | 3 4 | − | x | ) | ( | 1 2 | + | x | ) | = | 0 |
| Left side of the equation = | 3 4 | ( | 80 | ÷ | 41 | − | x | ) | − | x | ( | 80 | ÷ | 41 | − | x | ) | − | ( | 1 2 | + | x | ) | ( | 80 | ÷ | 41 | − | x | ) | − | ( | 3 4 | − | x | ) | ( | 1 2 | + | x | ) |
| = | 3 4 | × | 80 | ÷ | 41 | − | 3 4 | x | − | x | ( | 80 | ÷ | 41 | − | x | ) | − | ( | 1 2 | + | x | ) | ( | 80 | ÷ | 41 | − | x | ) | − | ( | 3 4 | − | x | ) | ( | 1 2 | + | x | ) |
| = | 60 41 | − | 3 4 | x | − | x | ( | 80 | ÷ | 41 | − | x | ) | − | ( | 1 2 | + | x | ) | ( | 80 | ÷ | 41 | − | x | ) | − | ( | 3 4 | − | x | ) | ( | 1 2 | + | x | ) |
| = | 60 41 | − | 3 4 | x | − | x | × | 80 | ÷ | 41 | + | x | x | − | ( | 1 2 | + | x | ) | ( | 80 | ÷ | 41 | − | x | ) | − | ( | 3 4 | − | x | ) | ( | 1 2 | + | x | ) |
| = | 60 41 | − | 3 4 | x | − | x | × | 80 41 | + | x | x | − | ( | 1 2 | + | x | ) | ( | 80 | ÷ | 41 | − | x | ) | − | ( | 3 4 | − | x | ) | ( | 1 2 | + | x | ) |
| = | 60 41 | − | 443 164 | x | + | x | x | − | ( | 1 2 | + | x | ) | ( | 80 | ÷ | 41 | − | x | ) | − | ( | 3 4 | − | x | ) | ( | 1 2 | + | x | ) |
| = | 60 41 | − | 443 164 | x | + | x | x | − | 1 2 | ( | 80 | ÷ | 41 | − | x | ) | − | x | ( | 80 | ÷ | 41 | − | x | ) | − | ( | 3 4 | − | x | ) | ( | 1 2 | + | x | ) |
| = | 60 41 | − | 443 164 | x | + | x | x | − | 1 2 | × | 80 | ÷ | 41 | + | 1 2 | x | − | x | ( | 80 | ÷ | 41 | − | x | ) |
| = | 60 41 | − | 443 164 | x | + | x | x | − | 40 41 | + | 1 2 | x | − | x | ( | 80 | ÷ | 41 | − | x | ) | − | ( | 3 4 | − | x | ) | ( | 1 2 | + | x | ) |
| = | 20 41 | − | 361 164 | x | + | x | x | − | x | ( | 80 | ÷ | 41 | − | x | ) | − | ( | 3 4 | − | x | ) | ( | 1 2 | + | x | ) |
| = | 20 41 | − | 361 164 | x | + | x | x | − | x | × | 80 | ÷ | 41 | + | x | x | − | ( | 3 4 | − | x | ) | ( | 1 2 | + | x | ) |
| = | 20 41 | − | 361 164 | x | + | x | x | − | x | × | 80 41 | + | x | x | − | ( | 3 4 | − | x | ) | ( | 1 2 | + | x | ) |
| = | 20 41 | − | 681 164 | x | + | x | x | + | x | x | − | ( | 3 4 | − | x | ) | ( | 1 2 | + | x | ) |
| = | 20 41 | − | 681 164 | x | + | x | x | + | x | x | − | 3 4 | ( | 1 2 | + | x | ) | + | x | ( | 1 2 | + | x | ) |
| = | 20 41 | − | 681 164 | x | + | x | x | + | x | x | − | 3 4 | × | 1 2 | − | 3 4 | x | + | x |
| = | 20 41 | − | 681 164 | x | + | x | x | + | x | x | − | 3 8 | − | 3 4 | x | + | x | ( | 1 2 | + | x | ) |
| = | 37 328 | − | 201 41 | x | + | x | x | + | x | x | + | x | ( | 1 2 | + | x | ) |
| = | 37 328 | − | 201 41 | x | + | x | x | + | x | x | + | x | × | 1 2 | + | x | x |
| = | 37 328 | − | 361 82 | x | + | x | x | + | x | x | + | x | x |
37 328 | − | 361 82 | x | + | x | x | + | x | x | + | x | x | = | 0 |
The solution of the equation:
x1≈0.026087 , keep 6 decimal places
x2≈1.441393 , keep 6 decimal places
There are 2 solution(s).
解程的详细方法请参阅：《方程的解法》