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    Current location:Equations > Monovariate Equation > The history of univariate equation calculation > Answer

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           ☆1 equations

[ 1/1 Equation]
    Work: Find the solution of equation 300000 = (x-26)*8*7*80+(1.5x-35)*8*7*40+(x-26)*12*7*70%*80+(1.5x-35)*12*7*60%*40+(1.5x-35)*16*12*7+(x-26)*18*12*7-713000 .
    Question type: Equation
    Solution:Original question:
     300000 = ( x 26) × 8 × 7 × 80 + (
3
2
x 35) × 8 × 7 × 40 + ( x 26) × 12 × 7 ×
70
100
     Right side of the equation = ( x 26) × 4480 + (
3
2
x 35) × 2240 + ( x 26) × 4704 + (
3
2
x 35) × 2016 + (
3
2
x 35) × 1344 + ( x 26) × 1512
    The equation is transformed into :
     300000 = ( x 26) × 4480 + (
3
2
x 35) × 2240 + ( x 26) × 4704 + (
3
2
x 35) × 2016 + (
3
2
x 35) × 1344 + ( x 26) × 1512
    Remove the bracket on the right of the equation:
     Right side of the equation = x × 448026 × 4480 + (
3
2
x 35) × 2240 + ( x 26) × 4704 + (
3
2
x 35) × 2016 + (
3
2
x 35) × 1344
                                               = x × 4480116480 + (
3
2
x 35) × 2240 + ( x 26) × 4704 + (
3
2
x 35) × 2016 + (
3
2
x 35) × 1344 + ( x 26)
                                               = 4480 x 829480 + (
3
2
x 35) × 2240 + ( x 26) × 4704 + (
3
2
x 35) × 2016 + (
3
2
x 35) × 1344 + ( x 26)
                                               = 4480 x 829480 +
3
2
x × 224035 × 2240 + ( x 26) × 4704 + (
3
2
x 35) × 2016
                                               = 4480 x 829480 + 3360 x 78400 + ( x 26) × 4704 + (
3
2
x 35) × 2016 + (
3
2
x 35) × 1344
                                               = 7840 x 907880 + ( x 26) × 4704 + (
3
2
x 35) × 2016 + (
3
2
x 35) × 1344 + ( x 26) × 1512
                                               = 7840 x 907880 + x × 470426 × 4704 + (
3
2
x 35) × 2016 + (
3
2
x 35) × 1344 + ( x 26)
                                               = 7840 x 907880 + x × 4704122304 + (
3
2
x 35) × 2016 + (
3
2
x 35) × 1344 + ( x 26) × 1512
                                               = 12544 x 1030184 + (
3
2
x 35) × 2016 + (
3
2
x 35) × 1344 + ( x 26) × 1512
                                               = 12544 x 1030184 +
3
2
x × 201635 × 2016 + (
3
2
x 35) × 1344 + ( x 26) × 1512
                                               = 12544 x 1030184 + 3024 x 70560 + (
3
2
x 35) × 1344 + ( x 26) × 1512
                                               = 15568 x 1100744 + (
3
2
x 35) × 1344 + ( x 26) × 1512
                                               = 15568 x 1100744 +
3
2
x × 134435 × 1344 + ( x 26) × 1512
                                               = 15568 x 1100744 + 2016 x 47040 + ( x 26) × 1512
                                               = 17584 x 1147784 + ( x 26) × 1512
                                               = 17584 x 1147784 + x × 151226 × 1512
                                               = 17584 x 1147784 + x × 151239312
                                               = 19096 x 1187096
    The equation is transformed into :
     300000 = 19096 x 1187096

    Transposition :
      - 19096 x = - 1187096300000

    Combine the items on the right of the equation:
      - 19096 x = - 1487096

    By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
     1487096 = 19096 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 :
     19096 x = 1487096

    The coefficient of the unknown number is reduced to 1 :
      x = 1487096 ÷ 19096
        = 1487096 ×
1
19096
        = 185887 ×
1
2387

    We obtained :
      x =
185887
2387
    This is the solution of the equation.

    Convert the result to decimal form :
      x = 77.874738



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