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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 3.14*3.14/8*(1-14.5/x)*(1-14.5/x)-1+20/x = 0 .
Question type: Equation
Solution:Original question:
157 50 | × | 157 50 | ÷ | 8 | × | ( | 1 | − | 29 2 | ÷ | x | ) | ( | 1 | − | 29 2 | ÷ | x | ) | − | 1 | + | 20 | ÷ | x | = | 0 |
| Multiply both sides of the equation by: | x |
157 50 | × | 157 50 | ÷ | 8 | × | ( | 1 | − | 29 2 | ÷ | x | ) | ( | 1 | − | 29 2 | ÷ | x | ) | x | − | 1 | x | + | 20 | = | 0 |
157 50 | × | 157 50 | ÷ | 8 | × | 1 | ( | 1 | − | 29 2 | ÷ | x | ) | x | − | 157 50 | × | 157 50 | ÷ | 8 | × | 29 2 | ÷ | x | × | ( | 1 | − | 29 2 | ÷ | x | ) | = | 0 |
24649 20000 | ( | 1 | − | 29 2 | ÷ | x | ) | x | − | 714821 40000 | ÷ | x | × | ( | 1 | − | 29 2 | ÷ | x | ) | x | − | 1 | x | + | 20 | = | 0 |
24649 20000 | × | 1 | x | − | 24649 20000 | × | 29 2 | ÷ | x | × | x | − | 714821 40000 | ÷ | 1 | × | ( | 1 | − | 29 2 | ÷ | x | ) | × | 1 | − | 1 | = | 0 |
24649 20000 | x | − | 714821 40000 | ÷ | x | × | x | − | 714821 40000 | ( | 1 | − | 29 2 | ÷ | x | ) | − | 1 | x | + | 20 | = | 0 |
4649 20000 | x | − | 714821 40000 | ÷ | x | × | x | − | 714821 40000 | ( | 1 | − | 29 2 | ÷ | x | ) | + | 20 | = | 0 |
4649 20000 | x | − | 714821 40000 | ÷ | 1 | × | 1 | − | 714821 40000 | × | 1 | + | 714821 40000 | × | 29 2 | ÷ | x | + | 20 | = | 0 |
4649 20000 | x | − | 714821 40000 | − | 714821 40000 | + | 20729809 80000 | ÷ | x | + | 20 | = | 0 |
4649 20000 | x | − | 314821 20000 | + | 20729809 80000 | ÷ | x | = | 0 |
| Multiply both sides of the equation by: | x |
4649 20000 | x | x | − | 314821 20000 | x | + | 20729809 80000 | = | 0 |
After the equation is converted into a general formula, there is a common factor:
( √350000x - √278925183 )
From
√350000x - √278925183 = 0
it is concluded that:：
| x1= | √278925183 √350000 |
Solutions that cannot be obtained by factorization:
x2≈39.488071 , keep 6 decimal places
There are 2 solution(s).
解程的详细方法请参阅：《方程的解法》