Mathematics
         
语言：中文    Language:English
Equations   
Fold
Unary equation
Multivariate equation
Math OP  
Unfold
Linear algebra      
Unfold
Derivative function
Function image
Hot issues
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.
    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 25950/（1+x/12*8)+25950/（1+x/12*9)+25950/（1+x/12*10)+25950/（1+x/12*11)+25950/（1+x/12*12) = 50000/（1+x/12*1） .
    Question type: Equation
    Solution:Original question:
     25950 ÷ (1 + x ÷ 12 × 8) + 25950 ÷ (1 + x ÷ 12 × 9) + 25950 ÷ (1 + x ÷ 12 × 10) + 25950 ÷ (1 + x ÷ 12 × 11) + 25950 ÷ (1 + x ÷ 12 × 12) = 50000 ÷ (1 + x ÷ 12 × 1)
     Multiply both sides of the equation by:(1 + x ÷ 12 × 8) ,  (1 + x ÷ 12 × 1)
     25950(1 + x ÷ 12 × 1) + 25950 ÷ (1 + x ÷ 12 × 9) × (1 + x ÷ 12 × 8)(1 + x ÷ 12 × 1) + 25950 ÷ (1 + x ÷ 12 × 10) × (1 + x ÷ 12 × 8)(1 + x ÷ 12 × 1) + 25950 ÷ (1 + x ÷ 12 × 11) = 50000(1 + x ÷ 12 × 8)
    Remove a bracket on the left of the equation:：
     25950 × 1 + 25950 x ÷ 12 × 1 + 25950 ÷ (1 + x ÷ 12 × 9) × (1 + x ÷ 12 × 8)(1 + x ÷ 12 × 1) + 25950 ÷ (1 + x ÷ 12 × 10) = 50000(1 + x ÷ 12 × 8)
    Remove a bracket on the right of the equation:：
     25950 × 1 + 25950 x ÷ 12 × 1 + 25950 ÷ (1 + x ÷ 12 × 9) × (1 + x ÷ 12 × 8)(1 + x ÷ 12 × 1) + 25950 ÷ (1 + x ÷ 12 × 10) = 50000 × 1 + 50000 x ÷ 12 × 8
    The equation is reduced to :
     25950 +
4325
2
 x + 25950 ÷ (1 + x ÷ 12 × 9) × (1 + x ÷ 12 × 8)(1 + x ÷ 12 × 1) + 25950 ÷ (1 + x ÷ 12 × 10) × (1 + x ÷ 12 × 8)(1 + x ÷ 12 × 1) + 25950 = 50000 +
100000
3
 x
     Multiply both sides of the equation by:(1 + x ÷ 12 × 9)
     25950(1 + x ÷ 12 × 9) +
4325
2
 x (1 + x ÷ 12 × 9) + 25950(1 + x ÷ 12 × 8)(1 + x ÷ 12 × 1) + 25950 ÷ (1 + x ÷ 12 × 10) × (1 + x ÷ 12 × 8)(1 + x ÷ 12 × 1) = 50000(1 + x ÷ 12 × 9) +
100000
3
 x (1 + x ÷ 12 × 9)
    Remove a bracket on the left of the equation:
     25950 × 1 + 25950 x ÷ 12 × 9 +
4325
2
 x (1 + x ÷ 12 × 9) + 25950(1 + x ÷ 12 × 8)(1 + x ÷ 12 × 1) = 50000(1 + x ÷ 12 × 9) +
100000
3
 x (1 + x ÷ 12 × 9)
    Remove a bracket on the right of the equation:：
     25950 × 1 + 25950 x ÷ 12 × 9 +
4325
2
 x (1 + x ÷ 12 × 9) + 25950(1 + x ÷ 12 × 8)(1 + x ÷ 12 × 1) = 50000 × 1 + 50000 x ÷ 12 × 9 +
100000
3
 x (1 + x ÷ 12 × 9)
    The equation is reduced to :
     25950 +
38925
2
 x +
4325
2
 x (1 + x ÷ 12 × 9) + 25950(1 + x ÷ 12 × 8)(1 + x ÷ 12 × 1) + 25950 ÷ (1 + x ÷ 12 × 10) × (1 + x ÷ 12 × 8) = 50000 + 37500 x +
100000
3
 x (1 + x ÷ 12 × 9)
     Multiply both sides of the equation by:(1 + x ÷ 12 × 10)
     25950(1 + x ÷ 12 × 10) +
38925
2
 x (1 + x ÷ 12 × 10) +
4325
2
 x (1 + x ÷ 12 × 9)(1 + x ÷ 12 × 10) + 25950(1 + x ÷ 12 × 8)(1 + x ÷ 12 × 1) = 50000(1 + x ÷ 12 × 10) + 37500 x (1 + x ÷ 12 × 10) +
100000
3
 x (1 + x ÷ 12 × 9)(1 + x ÷ 12 × 10)
    Remove a bracket on the left of the equation:
     25950 × 1 + 25950 x ÷ 12 × 10 +
38925
2
 x (1 + x ÷ 12 × 10) +
4325
2
 x (1 + x ÷ 12 × 9) = 50000(1 + x ÷ 12 × 10) + 37500 x (1 + x ÷ 12 × 10) +
100000
3
 x (1 + x ÷ 12 × 9)(1 + x ÷ 12 × 10)
    Remove a bracket on the right of the equation:：
     25950 × 1 + 25950 x ÷ 12 × 10 +
38925
2
 x (1 + x ÷ 12 × 10) +
4325
2
 x (1 + x ÷ 12 × 9) = 50000 × 1 + 50000 x ÷ 12 × 10 + 37500 x (1 + x ÷ 12 × 10) +
100000
3
 x (1 + x ÷ 12 × 9)
    The equation is reduced to :
     25950 + 21625 x +
38925
2
 x (1 + x ÷ 12 × 10) +
4325
2
 x (1 + x ÷ 12 × 9)(1 + x ÷ 12 × 10) + 25950(1 + x ÷ 12 × 8) = 50000 +
125000
3
 x + 37500 x (1 + x ÷ 12 × 10) +
100000
3
 x (1 + x ÷ 12 × 9)(1 + x ÷ 12 × 10)
     Multiply both sides of the equation by:(1 + x ÷ 12 × 11)
     25950(1 + x ÷ 12 × 11) + 21625 x (1 + x ÷ 12 × 11) +
38925
2
 x (1 + x ÷ 12 × 10)(1 + x ÷ 12 × 11) +
4325
2
 x (1 + x ÷ 12 × 9) = 50000(1 + x ÷ 12 × 11) +
125000
3
 x (1 + x ÷ 12 × 11) + 37500 x (1 + x ÷ 12 × 10)(1 + x ÷ 12 × 11) +
100000
3
 x (1 + x ÷ 12 × 9)
    Remove a bracket on the left of the equation:
     25950 × 1 + 25950 x ÷ 12 × 11 + 21625 x (1 + x ÷ 12 × 11) +
38925
2
 x (1 + x ÷ 12 × 10) = 50000(1 + x ÷ 12 × 11) +
125000
3
 x (1 + x ÷ 12 × 11) + 37500 x (1 + x ÷ 12 × 10)(1 + x ÷ 12 × 11) +
100000
3
 x (1 + x ÷ 12 × 9)
    Remove a bracket on the right of the equation:：
     25950 × 1 + 25950 x ÷ 12 × 11 + 21625 x (1 + x ÷ 12 × 11) +
38925
2
 x (1 + x ÷ 12 × 10) = 50000 × 1 + 50000 x ÷ 12 × 11 +
125000
3
 x (1 + x ÷ 12 × 11) + 37500 x (1 + x ÷ 12 × 10)
    The equation is reduced to :
     25950 +
47575
2
 x + 21625 x (1 + x ÷ 12 × 11) +
38925
2
 x (1 + x ÷ 12 × 10)(1 + x ÷ 12 × 11) +
4325
2
 x = 50000 +
137500
3
 x +
125000
3
 x (1 + x ÷ 12 × 11) + 37500 x (1 + x ÷ 12 × 10)(1 + x ÷ 12 × 11) +
100000
3
 x
     Multiply both sides of the equation by:(1 + x ÷ 12 × 12)
     25950(1 + x ÷ 12 × 12) +
47575
2
 x (1 + x ÷ 12 × 12) + 21625 x (1 + x ÷ 12 × 11)(1 + x ÷ 12 × 12) +
38925
2
 x (1 + x ÷ 12 × 10) = 50000(1 + x ÷ 12 × 12) +
137500
3
 x (1 + x ÷ 12 × 12) +
125000
3
 x (1 + x ÷ 12 × 11)(1 + x ÷ 12 × 12) + 37500 x (1 + x ÷ 12 × 10)
    Remove a bracket on the left of the equation:
     25950 × 1 + 25950 x ÷ 12 × 12 +
47575
2
 x (1 + x ÷ 12 × 12) + 21625 x (1 + x ÷ 12 × 11) = 50000(1 + x ÷ 12 × 12) +
137500
3
 x (1 + x ÷ 12 × 12) +
125000
3
 x (1 + x ÷ 12 × 11)(1 + x ÷ 12 × 12) + 37500 x (1 + x ÷ 12 × 10)
    Remove a bracket on the right of the equation:：
     25950 × 1 + 25950 x ÷ 12 × 12 +
47575
2
 x (1 + x ÷ 12 × 12) + 21625 x (1 + x ÷ 12 × 11) = 50000 × 1 + 50000 x ÷ 12 × 12 +
137500
3
 x (1 + x ÷ 12 × 12) +
125000
3
 x (1 + x ÷ 12 × 11)

    The solution of the equation:
        x1≈-1.140488 , keep 6 decimal places
        x2≈2.633940 , keep 6 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 go to the Hot Problems section！


Return



  New addition:Lenders ToolBox module（Specific location：Math OP > Lenders ToolBox ），welcome。