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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 0.53*(2-0.53)*q*(2-q)+(1-0.53)*(1-0.53)*q*(2-q)+0.53*(2-0.53)*(1-q)*(1-q)+(1-0.53)*(1-0.53)*(1-q)*(1-q) = 1 .
Question type: Equation
Solution:Original question:
Remove the bracket on the left of the equation:
After the equation is converted into a general formula, it is converted into:
( 125000q + 86631 )( 1000000q + 570739 )( 1665q + 863 )( 500000q + 154321 )( 200000q + 45753 )( 62500q - 679 )( 62500q - 679 )( 1000000q - 90741 )( 500000q - 125247 )( 1000000q - 410247 )=0
From
125000q + 86631 = 0
1000000q + 570739 = 0
1665q + 863 = 0
500000q + 154321 = 0
200000q + 45753 = 0
62500q - 679 = 0
62500q - 679 = 0
1000000q - 90741 = 0
500000q - 125247 = 0
1000000q - 410247 = 0
it is concluded that:：
There are 10 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 0.53*(2-0.53)*q*(2-q)+(1-0.53)*(1-0.53)*q*(2-q)+0.53*(2-0.53)*(1-q)*(1-q)+(1-0.53)*(1-0.53)*(1-q)*(1-q) = 1 .
Question type: Equation
Solution:Original question:
53 100 | ( | 2 | − | 53 100 | ) | q | ( | 2 | − | q | ) | + | ( | 1 | − | 53 100 | ) | ( | 1 | − | 53 100 | ) | q | ( | 2 | − | q | ) | + | 53 100 | ( | 2 | − | 53 100 | ) | ( | 1 | − | q | ) | ( | 1 | − | q | ) | = | 1 |
| Left side of the equation = | 53 100 | × | 2 | q | ( | 2 | − | q | ) | − | 53 100 | × | 53 100 | q | ( | 2 | − | q | ) | + | ( | 1 | − | 53 100 | ) | ( | 1 | − | 53 100 | ) | q | ( | 2 | − | q | ) |
| = | 53 50 | q | ( | 2 | − | q | ) | − | 2809 10000 | q | ( | 2 | − | q | ) | + | ( | 1 | − | 53 100 | ) | ( | 1 | − | 53 100 | ) | q | ( | 2 | − | q | ) | + | 53 100 | ( | 2 | − | 53 100 | ) |
| = | 53 50 | q | × | 2 | − | 53 50 | q | q | − | 2809 10000 | q | ( | 2 | − | q | ) | + | ( | 1 | − | 53 100 | ) | ( | 1 | − | 53 100 | ) | q |
| = | 53 25 | q | − | 53 50 | q | q | − | 2809 10000 | q | ( | 2 | − | q | ) | + | ( | 1 | − | 53 100 | ) | ( | 1 | − | 53 100 | ) | q | ( | 2 | − | q | ) |
| = | 53 25 | q | − | 53 50 | q | q | − | 2809 10000 | q | × | 2 | + | 2809 10000 | q | q | + | ( | 1 | − | 53 100 | ) |
| = | 53 25 | q | − | 53 50 | q | q | − | 2809 5000 | q | + | 2809 10000 | q | q | + | ( | 1 | − | 53 100 | ) | ( | 1 | − | 53 100 | ) |
| = | 7791 5000 | q | − | 53 50 | q | q | + | 2809 10000 | q | q | + | ( | 1 | − | 53 100 | ) | ( | 1 | − | 53 100 | ) | q | ( | 2 | − | q | ) |
| = | 7791 5000 | q | − | 53 50 | q | q | + | 2809 10000 | q | q | + | 1 | ( | 1 | − | 53 100 | ) | q | ( | 2 | − | q | ) |
| = | 7791 5000 | q | − | 53 50 | q | q | + | 2809 10000 | q | q | + | 1 | × | 1 | q | ( | 2 | − | q | ) |
| = | 7791 5000 | q | − | 53 50 | q | q | + | 2809 10000 | q | q | + | 1 | q | ( | 2 | − | q | ) | − | 53 100 |
| = | 7791 5000 | q | − | 53 50 | q | q | + | 2809 10000 | q | q | + | 1 | q | × | 2 | − | 1 |
| = | 7791 5000 | q | − | 53 50 | q | q | + | 2809 10000 | q | q | + | 2 | q | − | 1 | q |
| = | 17791 5000 | q | − | 53 50 | q | q | + | 2809 10000 | q | q | − | 1 | q | q | − | 53 100 |
| = | 17791 5000 | q | − | 53 50 | q | q | + | 2809 10000 | q | q | − | 1 | q | q | − | 53 100 |
| = | 17791 5000 | q | − | 53 50 | q | q | + | 2809 10000 | q | q | − | 1 | q | q | − | 53 50 |
| = | 12491 5000 | q | − | 53 50 | q | q | + | 2809 10000 | q | q | − | 1 | q | q | + | 53 100 |
| = | 12491 5000 | q | − | 53 50 | q | q | + | 2809 10000 | q | q | − | 1 | q | q | + | 53 100 |
| = | 12491 5000 | q | − | 53 50 | q | q | + | 2809 10000 | q | q | − | 1 | q | q | + | 53 100 |
| = | 12491 5000 | q | − | 53 50 | q | q | + | 2809 10000 | q | q | − | 1 | q | q | + | 53 100 |
| = | 12491 5000 | q | − | 53 50 | q | q | + | 2809 10000 | q | q | − | 1 | q | q | + | 53 100 |
| = | 7191 5000 | q | − | 53 50 | q | q | + | 2809 10000 | q | q | − | 1 | q | q | + | 53 100 |
| = | 7191 5000 | q | − | 53 50 | q | q | + | 2809 10000 | q | q | − | 1 | q | q | + | 53 100 |
| = | 7191 5000 | q | − | 53 50 | q | q | + | 2809 10000 | q | q | − | 1 | q | q | + | 53 100 |
| = | 2 | q | − | 53 50 | q | q | + | 2809 10000 | q | q | − | 1 | q | q | + | 53 100 |
| = | 2 | q | − | 53 50 | q | q | + | 2809 10000 | q | q | − | 1 | q | q | + | 53 100 |
After the equation is converted into a general formula, it is converted into:
( 125000q + 86631 )( 1000000q + 570739 )( 1665q + 863 )( 500000q + 154321 )( 200000q + 45753 )( 62500q - 679 )( 62500q - 679 )( 1000000q - 90741 )( 500000q - 125247 )( 1000000q - 410247 )=0
From
125000q + 86631 = 0
1000000q + 570739 = 0
1665q + 863 = 0
500000q + 154321 = 0
200000q + 45753 = 0
62500q - 679 = 0
62500q - 679 = 0
1000000q - 90741 = 0
500000q - 125247 = 0
1000000q - 410247 = 0
it is concluded that:：
| q1= | - | 86631 125000 |
| q2= | - | 570739 1000000 |
| q3= | - | 863 1665 |
| q4= | - | 154321 500000 |
| q5= | - | 45753 200000 |
| q6= | 679 62500 |
| q7= | 679 62500 |
| q8= | 90741 1000000 |
| q9= | 125247 500000 |
| q10= | 410247 1000000 |
There are 10 solution(s).
解程的详细方法请参阅：《方程的解法》