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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 5 = (5.1*p+4.9020*（1-p）)/1.01 .
Question type: Equation
Solution:Original question:
| 5 | = | ( | 51 10 | p | + | 2451 500 | ( | 1 | − | p | ) | ) | ÷ | 101 100 |
| Right side of the equation = | 51 10 | p | × | 100 101 | + | 2451 500 | ( | 1 | − | p | ) | × | 100 101 |
| = | 510 101 | p | + | 2451 505 | ( | 1 | − | p | ) |
| = | 510 101 | p | + | 2451 505 | × | 1 | − | 2451 505 | p |
| = | 510 101 | p | + | 2451 505 | − | 2451 505 | p |
| = | 9999 51005 | p | + | 2451 505 |
| 5 | = | 9999 51005 | p | + | 2451 505 |
Transposition :
| - | 9999 51005 | p | = | 2451 505 | − | 5 |
Combine the items on the right of the equation:
| - | 9999 51005 | p | = | - | 74 505 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
74 505 | = | 9999 51005 | p |
If the left side of the equation is equal to the right side, then the right side must also be equal to the left side, that is :
9999 51005 | p | = | 74 505 |
The coefficient of the unknown number is reduced to 1 :
| p | = | 74 505 | ÷ | 9999 51005 |
| = | 74 505 | × | 51005 9999 |
| = | 74 101 | × | 10201 9999 |
We obtained :
| p | = | 754874 1009899 |
By reducing fraction, we can get:
| p | = | 7474 9999 |
Convert the result to decimal form :
| p | = | 0.747475 |