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    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 5720*x+183240 = (360*509)/(0.518-0.8)*(x/550-0.8)+(360*1520)/(0.518-0.8)*(x/800-0.8)+(360*509)/(0.518-0.8)*(x/300-0.8) .
    Question type: Equation
    Solution:Original question:
     5720 x + 183240 = (360 × 509) ÷ (
259
500
 −
4
5
) × ( x ÷ 550 −
4
5
) + (360 × 1520) ÷ (
259
500
 −
4
5
) × ( x ÷ 800 −
4
5
) + (360 × 509) ÷ (
259
500
 −
4
5
) × ( x ÷ 300 −
4
5
)
     Multiply both sides of the equation by:(
259
500
 −
4
5
)
     5720 x (
259
500
 −
4
5
) + 183240(
259
500
 −
4
5
) = (360 × 509)( x ÷ 550 −
4
5
) + (360 × 1520) ÷ (
259
500
 −
4
5
) × ( x ÷ 800 −
4
5
)(
259
500
 −
4
5
) + (360 × 509) ÷ (
259
500
 −
4
5
) × ( x ÷ 300 −
4
5
)(
259
500
 −
4
5
)
    Remove a bracket on the left of the equation:：
     5720 x ×
259
500
 − 5720 x ×
4
5
 + 183240(
259
500
 −
4
5
) = (360 × 509)( x ÷ 550 −
4
5
) + (360 × 1520) ÷ (
259
500
 −
4
5
) × ( x ÷ 800 −
4
5
)(
259
500
 −
4
5
) + (360 × 509) ÷ (
259
500
 −
4
5
) × ( x ÷ 300 −
4
5
)(
259
500
 −
4
5
)
    Remove a bracket on the right of the equation:：
     5720 x ×
259
500
 − 5720 x ×
4
5
 + 183240(
259
500
 −
4
5
) = 360 × 509( x ÷ 550 −
4
5
) + (360 × 1520) ÷ (
259
500
 −
4
5
) × ( x ÷ 800 −
4
5
)(
259
500
 −
4
5
) + (360 × 509) ÷ (
259
500
 −
4
5
) × ( x ÷ 300 −
4
5
)(
259
500
 −
4
5
)
    The equation is reduced to :
     
74074
25
 x − 4576 x + 183240(
259
500
 −
4
5
) = 183240( x ÷ 550 −
4
5
) + (360 × 1520) ÷ (
259
500
 −
4
5
) × ( x ÷ 800 −
4
5
)(
259
500
 −
4
5
) + (360 × 509) ÷ (
259
500
 −
4
5
) × ( x ÷ 300 −
4
5
)(
259
500
 −
4
5
)
    The equation is reduced to :
      -
40326
25
 x + 183240(
259
500
 −
4
5
) = 183240( x ÷ 550 −
4
5
) + (360 × 1520) ÷ (
259
500
 −
4
5
) × ( x ÷ 800 −
4
5
)(
259
500
 −
4
5
) + (360 × 509) ÷ (
259
500
 −
4
5
) × ( x ÷ 300 −
4
5
)(
259
500
 −
4
5
)
     Multiply both sides of the equation by:(
259
500
 −
4
5
)
      -
40326
25
 x (
259
500
 −
4
5
) + 183240(
259
500
 −
4
5
)(
259
500
 −
4
5
) = 183240( x ÷ 550 −
4
5
)(
259
500
 −
4
5
) + (360 × 1520)( x ÷ 800 −
4
5
)(
259
500
 −
4
5
) + (360 × 509) ÷ (
259
500
 −
4
5
) × ( x ÷ 300 −
4
5
)(
259
500
 −
4
5
)(
259
500
 −
4
5
)
    Remove a bracket on the left of the equation:
      -
40326
25
 x ×
259
500
 +
40326
25
 x ×
4
5
 + 183240(
259
500
 −
4
5
)(
259
500
 −
4
5
) = 183240( x ÷ 550 −
4
5
)(
259
500
 −
4
5
) + (360 × 1520)( x ÷ 800 −
4
5
)(
259
500
 −
4
5
) + (360 × 509) ÷ (
259
500
 −
4
5
) × ( x ÷ 300 −
4
5
)(
259
500
 −
4
5
)(
259
500
 −
4
5
)
    Remove a bracket on the right of the equation:：
      -
40326
25
 x ×
259
500
 +
40326
25
 x ×
4
5
 + 183240(
259
500
 −
4
5
)(
259
500
 −
4
5
) = 183240 x ÷ 550 × (
259
500
 −
4
5
) − 183240 ×
4
5
(
259
500
 −
4
5
) + (360 × 1520)( x ÷ 800 −
4
5
)(
259
500
 −
4
5
) + (360 × 509) ÷ (
259
500
 −
4
5
)
    The equation is reduced to :
      -
5222217
6250
 x +
161304
125
 x + 183240(
259
500
 −
4
5
)(
259
500
 −
4
5
) =
18324
55
 x (
259
500
 −
4
5
) − 146592(
259
500
 −
4
5
) + (360 × 1520)( x ÷ 800 −
4
5
)(
259
500
 −
4
5
) + (360 × 509) ÷ (
259
500
 −
4
5
) × ( x ÷ 300 −
4
5
)(
259
500
 −
4
5
)
    The equation is reduced to :
     
2842983
6250
 x + 183240(
259
500
 −
4
5
)(
259
500
 −
4
5
) =
18324
55
 x (
259
500
 −
4
5
) − 146592(
259
500
 −
4
5
) + (360 × 1520)( x ÷ 800 −
4
5
)(
259
500
 −
4
5
) + (360 × 509) ÷ (
259
500
 −
4
5
) × ( x ÷ 300 −
4
5
)(
259
500
 −
4
5
)
     Multiply both sides of the equation by:(
259
500
 −
4
5
)
     
2842983
6250
 x (
259
500
 −
4
5
) + 183240(
259
500
 −
4
5
)(
259
500
 −
4
5
)(
259
500
 −
4
5
) =
18324
55
 x (
259
500
 −
4
5
)(
259
500
 −
4
5
) − 146592(
259
500
 −
4
5
)(
259
500
 −
4
5
) + (360 × 1520)( x ÷ 800 −
4
5
)(
259
500
 −
4
5
)(
259
500
 −
4
5
) + (360 × 509)
    Remove a bracket on the left of the equation:
     
2842983
6250
 x ×
259
500
 −
2842983
6250
 x ×
4
5
 + 183240(
259
500
 −
4
5
)(
259
500
 −
4
5
)(
259
500
 −
4
5
) =
18324
55
 x (
259
500
 −
4
5
)(
259
500
 −
4
5
) − 146592(
259
500
 −
4
5
)(
259
500
 −
4
5
) + (360 × 1520)( x ÷ 800 −
4
5
)(
259
500
 −
4
5
)(
259
500
 −
4
5
) + (360 × 509)
    Remove a bracket on the right of the equation:：
     
2842983
6250
 x ×
259
500
 −
2842983
6250
 x ×
4
5
 + 183240(
259
500
 −
4
5
)(
259
500
 −
4
5
)(
259
500
 −
4
5
) =
18324
55
 x ×
259
500
(
259
500
 −
4
5
) −
18324
55
 x ×
4
5
(
259
500
 −
4
5
) − 146592(
259
500
 −
4
5
)(
259
500
 −
4
5
) + (360 × 1520)
    The equation is reduced to :
     
736332597
3125000
 x −
5685966
15625
 x + 183240(
259
500
 −
4
5
)(
259
500
 −
4
5
)(
259
500
 −
4
5
) =
1186479
6875
 x (
259
500
 −
4
5
) −
73296
275
 x (
259
500
 −
4
5
) − 146592(
259
500
 −
4
5
)(
259
500
 −
4
5
) + (360 × 1520)( x ÷ 800 −
4
5
)(
259
500
 −
4
5
)

    
        x≈209.586411 , keep 6 decimal places    
    There are 1 solution(s).

解一元一次方程的详细方法请参阅：《一元一次方程的解法》


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