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           ☆1 equations

[ 1/1 Equation]
    Work: Find the solution of equation 7600/(107*0.22+x)+10000/x+10000/(x+107*0.1) = 150 .
    Question type: Equation
    Solution:Original question:
     7600 ÷ (107 ×
11
50
+ x ) + 10000 ÷ x + 10000 ÷ ( x + 107 ×
1
10
) = 150
     Multiply both sides of the equation by:(107 ×
11
50
+ x )
     7600 + 10000 ÷ x × (107 ×
11
50
+ x ) + 10000 ÷ ( x + 107 ×
1
10
) × (107 ×
11
50
+ x ) = 150(107 ×
11
50
+ x )
    Remove a bracket on the left of the equation::
     7600 + 10000 ÷ x × 107 ×
11
50
+ 10000 ÷ x × x + 10000 ÷ ( x + 107 ×
1
10
) × (107 ×
11
50
+ x ) = 150(107 ×
11
50
+ x )
    Remove a bracket on the right of the equation::
     7600 + 10000 ÷ x × 107 ×
11
50
+ 10000 ÷ x × x + 10000 ÷ ( x + 107 ×
1
10
) × (107 ×
11
50
+ x ) = 150 × 107 ×
11
50
+ 150 x
    The equation is reduced to :
     7600 + 235400 ÷ x + 10000 ÷ x × x + 10000 ÷ ( x + 107 ×
1
10
) × (107 ×
11
50
+ x ) = 3531 + 150 x
     Multiply both sides of the equation by: x
     7600 x + 235400 + 10000 ÷ 1 × 1 x + 10000 ÷ ( x + 107 ×
1
10
) × (107 ×
11
50
+ x ) x = 3531 x + 150 x x
    Remove a bracket on the left of the equation:
     7600 x + 235400 + 10000 ÷ 1 × 1 x + 10000 ÷ ( x + 107 ×
1
10
) × 107 ×
11
50
x = 3531 x + 150 x x
    The equation is reduced to :
     7600 x + 235400 + 10000 x + 235400 ÷ ( x + 107 ×
1
10
) × x + 10000 ÷ ( x + 107 ×
1
10
) × x x = 3531 x + 150 x x
    The equation is reduced to :
     17600 x + 235400 + 235400 ÷ ( x + 107 ×
1
10
) × x + 10000 ÷ ( x + 107 ×
1
10
) × x x = 3531 x + 150 x x
     Multiply both sides of the equation by:( x + 107 ×
1
10
)
     17600 x ( x + 107 ×
1
10
) + 235400( x + 107 ×
1
10
) + 235400 x + 10000 x x = 3531 x ( x + 107 ×
1
10
) + 150 x x ( x + 107 ×
1
10
)
    Remove a bracket on the left of the equation:
     17600 x x + 17600 x × 107 ×
1
10
+ 235400( x + 107 ×
1
10
) + 235400 x + 10000 = 3531 x ( x + 107 ×
1
10
) + 150 x x ( x + 107 ×
1
10
)
    Remove a bracket on the right of the equation::
     17600 x x + 17600 x × 107 ×
1
10
+ 235400( x + 107 ×
1
10
) + 235400 x + 10000 = 3531 x x + 3531 x × 107 ×
1
10
+ 150 x x ( x + 107 ×
1
10
)
    The equation is reduced to :
     17600 x x + 188320 x + 235400( x + 107 ×
1
10
) + 235400 x + 10000 x x = 3531 x x +
377817
10
x + 150 x x ( x + 107 ×
1
10
)
    The equation is reduced to :
     17600 x x + 423720 x + 235400( x + 107 ×
1
10
) + 10000 x x = 3531 x x +
377817
10
x + 150 x x ( x + 107 ×
1
10
)
    Remove a bracket on the left of the equation:
     17600 x x + 423720 x + 235400 x + 235400 × 107 ×
1
10
+ 10000 x = 3531 x x +
377817
10
x + 150 x x ( x + 107 ×
1
10
)
    Remove a bracket on the right of the equation::
     17600 x x + 423720 x + 235400 x + 235400 × 107 ×
1
10
+ 10000 x = 3531 x x +
377817
10
x + 150 x x x + 150 x x
    The equation is reduced to :
     17600 x x + 423720 x + 235400 x + 2518780 + 10000 x x = 3531 x x +
377817
10
x + 150 x x x + 1605 x x
    The equation is reduced to :
     17600 x x + 659120 x + 2518780 + 10000 x x = 3531 x x +
377817
10
x + 150 x x x + 1605 x x

    The solution of the equation:
        x1≈-19.365175 , keep 6 decimal places
        x2≈-4.980407 , keep 6 decimal places
        x3≈174.105582 , keep 6 decimal places
    
    There are 3 solution(s).


解程的详细方法请参阅:《方程的解法》



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