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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 (x-290)*(1-25%)/1410 = (x-170)*(1-25%)-258.75/1210 .
Question type: Equation
Solution:Original question:
| ( | x | − | 290 | ) | ( | 1 | − | 25 100 | ) | ÷ | 1410 | = | ( | x | − | 170 | ) | ( | 1 | − | 25 100 | ) | − | 1035 4 | ÷ | 1210 |
| Left side of the equation = | x | ( | 1 | − | 25 100 | ) | × | 1 1410 | − | 290 | ( | 1 | − | 25 100 | ) | × | 1 1410 |
| = | x | ( | 1 | − | 25 100 | ) | × | 1 1410 | − | 29 141 | ( | 1 | − | 25 100 | ) |
| = | x | × | 1 | × | 1 1410 | − | x | × | 25 100 | × | 1 1410 | − | 29 141 | ( | 1 | − | 25 100 | ) |
| = | x | × | 1 1410 | − | x | × | 1 5640 | − | 29 141 | ( | 1 | − | 25 100 | ) |
| = | 1 1880 | x | − | 29 141 | ( | 1 | − | 25 100 | ) |
| = | 1 1880 | x | − | 29 141 | × | 1 | + | 29 141 | × | 25 100 |
| = | 1 1880 | x | − | 29 141 | + | 29 564 |
| = | 1 1880 | x | − | 1363 8836 |
1 1880 | x | − | 1363 8836 | = | ( | x | − | 170 | ) | ( | 1 | − | 25 100 | ) | − | 1035 4 | ÷ | 1210 |
| Right side of the equation = | ( | x | − | 170 | ) | ( | 1 | − | 25 100 | ) | − | 207 968 |
1 1880 | x | − | 1363 8836 | = | ( | x | − | 170 | ) | ( | 1 | − | 25 100 | ) | − | 207 968 |
| Right side of the equation = | x | ( | 1 | − | 25 100 | ) | − | 170 | ( | 1 | − | 25 100 | ) | − | 207 968 |
| = | x | × | 1 | − | x | × | 25 100 | − | 170 | ( | 1 | − | 25 100 | ) | − | 207 968 |
| = | 3 4 | x | − | 170 | ( | 1 | − | 25 100 | ) | − | 207 968 |
| = | 3 4 | x | − | 170 | × | 1 | + | 170 | × | 25 100 | − | 207 968 |
| = | 3 4 | x | − | 170 | + | 85 2 | − | 207 968 |
| = | 3 4 | x | − | 123627 968 |
1 1880 | x | − | 1363 8836 | = | 3 4 | x | − | 123627 968 |
Transposition :
1 1880 | x | − | 3 4 | x | = | - | 123627 968 | + | 1363 8836 |
Combine the items on the left of the equation:
| - | 1409 1880 | x | = | - | 123627 968 | + | 1363 8836 |
Combine the items on the right of the equation:
| - | 1409 1880 | x | = | - | 5803451 45496 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
5803451 45496 | = | 1409 1880 | x |
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 :
1409 1880 | x | = | 5803451 45496 |
The coefficient of the unknown number is reduced to 1 :
| x | = | 5803451 45496 | ÷ | 1409 1880 |
| = | 5803451 45496 | × | 1880 1409 |
| = | 5803451 5687 | × | 235 1409 |
We obtained :
| x | = | 1363810985 8012983 |
By reducing fraction, we can get:
| x | = | 29017255 170489 |
Convert the result to decimal form :
| x | = | 170.20016 |