Mathematics
语言：中文
Language:English

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*（1-075x%）*2500*(1+2.5x%)+4500*7 = (4500*7+2500*5)*[1+(5/11)x%] .
    Question type: Equation
    Solution:Original question:
     5(1 − 75 x ) × 2500(1 +
5
2
 x ) + 4500 × 7 = (4500 × 7 + 2500 × 5)(1 + (5 ÷ 11) x )
     Left side of the equation = 12500(1 − 75 x )(1 +
5
2
 x ) + 31500
    The equation is transformed into :
     12500(1 − 75 x )(1 +
5
2
 x ) + 31500 = (4500 × 7 + 2500 × 5)(1 + (5 ÷ 11) x )
    Remove the bracket on the left of the equation:
     Left side of the equation = 12500 × 1(1 +
5
2
 x ) − 12500 × 75 x (1 +
5
2
 x ) + 31500
                                             = 12500(1 +
5
2
 x ) − 937500 x (1 +
5
2
 x ) + 31500
                                             = 12500 × 1 + 12500 ×
5
2
 x − 937500 x (1 +
5
2
 x ) + 31500
                                             = 12500 + 31250 x − 937500 x (1 +
5
2
 x ) + 31500
                                             = 44000 + 31250 x − 937500 x (1 +
5
2
 x )
                                             = 44000 + 31250 x − 937500 x × 1 − 937500 x ×
5
2
 x
                                             = 44000 + 31250 x − 937500 x − 2343750 x x
                                             = 44000 − 906250 x − 2343750 x x
    The equation is transformed into :
     44000 − 906250 x − 2343750 x x = (4500 × 7 + 2500 × 5)(1 + (5 ÷ 11) x )
    Remove the bracket on the right of the equation:
     Right side of the equation = 4500 × 7(1 + (5 ÷ 11) x ) + 2500 × 5(1 + (5 ÷ 11) x )
                                               = 31500(1 + (5 ÷ 11) x ) + 12500(1 + (5 ÷ 11) x )
                                               = 31500 × 1 + 31500(5 ÷ 11) x + 12500(1 + (5 ÷ 11) x )
                                               = 31500 + 31500(5 ÷ 11) x + 12500(1 + (5 ÷ 11) x )
                                               = 31500 + 31500 × 5 ÷ 11 × x + 12500(1 + (5 ÷ 11) x )
                                               = 31500 +
157500
11
 x + 12500(1 + (5 ÷ 11) x )
                                               = 31500 +
157500
11
 x + 12500 × 1 + 12500(5 ÷ 11) x
                                               = 31500 +
157500
11
 x + 12500 + 12500(5 ÷ 11) x
                                               = 44000 +
157500
11
 x + 12500(5 ÷ 11) x
                                               = 44000 +
157500
11
 x + 12500 × 5 ÷ 11 × x
                                               = 44000 +
157500
11
 x +
62500
11
 x
                                               = 44000 + 20000 x
    The equation is transformed into :
     44000 − 906250 x − 2343750 x x = 44000 + 20000 x

    After the equation is converted into a general formula, there is a common factor:
    ( x - 0 )
    From
        x - 0 = 0
    it is concluded that:：
        x1=0

    Solutions that cannot be obtained by factorization:
        x2≈-39.52 , keep 2 decimal places    
    There are 2 solution(s).

解程的详细方法请参阅：《方程的解法》



Your problem has not been solved here? Please take a look at the  hot problems ！


Return