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    Work: Find the solution of equation 0.069(5600＋x)5706-12(5706x＋106(5600＋x) ) = 0 .
    Question type: Equation
    Solution:Original question:

69 1000

(

5600

+

x

)

×

5706

−

12

(

5706

x

+

106

(

5600

+

x

)

)

=

0

Left side of the equation =

196857 500

(

5600

+

x

)

−

12

(

5706

x

+

106

(

5600

+

x

)

)

    The equation is transformed into :

196857 500

(

5600

+

x

)

−

12

(

5706

x

+

106

(

5600

+

x

)

)

=

0

    Remove the bracket on the left of the equation:

Left side of the equation =

196857 500

×

5600

+

196857 500

x

−

12

(

5706

x

+

106

(

5600

+

x

)

)

=

11023992 5

+

196857 500

x

−

12

(

5706

x

+

106

(

5600

+

x

)

)

=

11023992 5

+

196857 500

x

−

12

×

5706

x

−

12

×

106

(

5600

+

x

)

=

11023992 5

+

196857 500

x

−

68472

x

−

1272

(

5600

+

x

)

=

11023992 5

−

34039143 500

x

−

1272

(

5600

+

x

)

=

11023992 5

−

34039143 500

x

−

1272

×

5600

−

1272

x

=

11023992 5

−

34039143 500

x

−

7123200

−

1272

x

=

-

24592008 5

−

34675143 500

x

    The equation is transformed into :

-

24592008 5

−

34675143 500

x

=

0

    Transposition :

-

34675143 500

x

=

0

+

24592008 5

    Combine the items on the right of the equation:

-

34675143 500

x

=

24592008 5

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

-

24592008 5

=

34675143 500

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 :

34675143 500

x

=

-

24592008 5

    The coefficient of the unknown number is reduced to 1 :

x

=

-

24592008 5

÷

34675143 500

=

-

24592008 5

×

500 34675143

=

-

8197336

×

100 11558381

    We obtained :

x

=

-

819733600 11558381

    This is the solution of the equation.

    Convert the result to decimal form :

x

=

- 70.921144

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