Equations
Fold
Math OP
Unfold
Linear algebra
Unfold
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 [789*（1+0.466+0.0583x）+311]*[1.884+0.622+(20-x)] = 0 .
Question type: Equation
Solution:Original question:
| ( | 789 | ( | 1 | + | 233 500 | + | 583 10000 | x | ) | + | 311 | ) | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) | = | 0 |
| Left side of the equation = | 789 | ( | 1 | + | 233 500 | + | 583 10000 | x | ) | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) | + | 311 | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) |
| = | 789 | × | 1 | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) | + | 789 | × | 233 500 | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) | + | 789 | × | 583 10000 | x | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) | + | 311 | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) |
| = | 789 | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) | + | 183837 500 | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) | + | 459987 10000 | x | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) | + | 311 | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) |
| = | 789 | × | 471 250 | + | 789 | × | 311 500 | + | 789 | ( | 20 | − | x | ) | + | 183837 500 | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) | + | 459987 10000 | x | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) | + | 311 |
| = | 371619 250 | + | 245379 500 | + | 789 | ( | 20 | − | x | ) | + | 183837 500 | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) | + | 459987 10000 | x | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) | + | 311 | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) |
| = | 988617 500 | + | 789 | ( | 20 | − | x | ) | + | 183837 500 | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) | + | 459987 10000 | x | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) | + | 311 | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) |
| = | 988617 500 | + | 789 | × | 20 | − | 789 | x | + | 183837 500 | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) | + | 459987 10000 | x | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) | + | 311 | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) |
| = | 988617 500 | + | 15780 | − | 789 | x | + | 183837 500 | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) | + | 459987 10000 | x | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) | + | 311 | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) |
| = | 8878617 500 | − | 789 | x | + | 183837 500 | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) | + | 459987 10000 | x | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) | + | 311 | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) |
| = | 8878617 500 | − | 789 | x | + | 183837 500 | × | 471 250 | + | 183837 500 | × | 311 500 | + | 183837 500 | ( | 20 | − | x | ) | + | 459987 10000 | x | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) |
| = | 8878617 500 | − | 789 | x | + | 86587227 125000 | + | 57173307 250000 | + | 183837 500 | ( | 20 | − | x | ) | + | 459987 10000 | x | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) | + | 311 | ( | 471 250 | + | 311 500 | + | ( | 20 | − | x | ) | ) |
After the equation is converted into a general formula, there is a common factor:
( 500x - 11253 )
From
500x - 11253 = 0
it is concluded that:：
| x1= | 11253 500 |
Solutions that cannot be obtained by factorization:
x2≈-31.906858 , keep 6 decimal places
There are 2 solution(s).
解程的详细方法请参阅：《方程的解法》