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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 7500/(a+52+12.48+10.4)+10000/(a+52+10.4)+10000/(a+10.4)*3 = 143 .
    Question type: Equation
    Solution:Original question:
     7500 ÷ ( a + 52 +
312
25
+
52
5
) + 10000 ÷ ( a + 52 +
52
5
) + 10000 ÷ ( a +
52
5
) × 3 = 143
     Multiply both sides of the equation by:( a + 52 +
312
25
+
52
5
)
     7500 + 10000 ÷ ( a + 52 +
52
5
) × ( a + 52 +
312
25
+
52
5
) + 10000 ÷ ( a +
52
5
) × 3( a + 52 +
312
25
+
52
5
) = 143( a + 52 +
312
25
+
52
5
)
    Remove a bracket on the left of the equation::
     7500 + 10000 ÷ ( a + 52 +
52
5
) × a + 10000 ÷ ( a + 52 +
52
5
) × 52 + 10000 ÷ ( a + 52 +
52
5
) ×
312
25
+ 10000 ÷ ( a + 52 +
52
5
) = 143( a + 52 +
312
25
+
52
5
)
    Remove a bracket on the right of the equation::
     7500 + 10000 ÷ ( a + 52 +
52
5
) × a + 10000 ÷ ( a + 52 +
52
5
) × 52 + 10000 ÷ ( a + 52 +
52
5
) ×
312
25
+ 10000 ÷ ( a + 52 +
52
5
) = 143 a + 143 × 52 + 143 ×
312
25
+ 143 ×
52
5
    The equation is reduced to :
     7500 + 10000 ÷ ( a + 52 +
52
5
) × a + 520000 ÷ ( a + 52 +
52
5
) + 124800 ÷ ( a + 52 +
52
5
) + 104000 ÷ ( a + 52 +
52
5
) + 30000 ÷ ( a +
52
5
) = 143 a + 7436 +
44616
25
+
7436
5
    The equation is reduced to :
     7500 + 10000 ÷ ( a + 52 +
52
5
) × a + 520000 ÷ ( a + 52 +
52
5
) + 124800 ÷ ( a + 52 +
52
5
) + 104000 ÷ ( a + 52 +
52
5
) + 30000 ÷ ( a +
52
5
) = 143 a +
267696
25
     Multiply both sides of the equation by:( a + 52 +
52
5
)
     7500( a + 52 +
52
5
) + 10000 a + 520000 + 124800 + 104000 + 30000 ÷ ( a +
52
5
) × ( a + 52 +
312
25
+
52
5
)( a + 52 +
52
5
) = 143 a ( a + 52 +
52
5
) +
267696
25
( a + 52 +
52
5
)
    Remove a bracket on the left of the equation:
     7500 a + 7500 × 52 + 7500 ×
52
5
+ 10000 a + 520000 + 124800 + 104000 + 30000 = 143 a ( a + 52 +
52
5
) +
267696
25
( a + 52 +
52
5
)
    Remove a bracket on the right of the equation::
     7500 a + 7500 × 52 + 7500 ×
52
5
+ 10000 a + 520000 + 124800 + 104000 + 30000 = 143 a a + 143 a × 52 + 143 a ×
52
5
+
267696
25
( a + 52 +
52
5
)
    The equation is reduced to :
     7500 a + 390000 + 78000 + 10000 a + 520000 + 124800 + 104000 + 30000 ÷ ( a +
52
5
) × ( a + 52 +
312
25
+
52
5
) = 143 a a + 7436 a +
7436
5
a +
267696
25
( a + 52 +
52
5
)
    The equation is reduced to :
     17500 a + 1216800 + 30000 ÷ ( a +
52
5
) × ( a + 52 +
312
25
+
52
5
)( a + 52 +
52
5
) = 143 a a +
44616
5
a +
267696
25
( a + 52 +
52
5
)
     Multiply both sides of the equation by:( a +
52
5
)
     17500 a ( a +
52
5
) + 1216800( a +
52
5
) + 30000( a + 52 +
312
25
+
52
5
)( a + 52 +
52
5
) = 143 a a ( a +
52
5
) +
44616
5
a ( a +
52
5
) +
267696
25
( a + 52 +
52
5
)( a +
52
5
)
    Remove a bracket on the left of the equation:
     17500 a a + 17500 a ×
52
5
+ 1216800( a +
52
5
) + 30000( a + 52 +
312
25
+
52
5
)( a + 52 +
52
5
) = 143 a a ( a +
52
5
) +
44616
5
a ( a +
52
5
) +
267696
25
( a + 52 +
52
5
)( a +
52
5
)
    Remove a bracket on the right of the equation::
     17500 a a + 17500 a ×
52
5
+ 1216800( a +
52
5
) + 30000( a + 52 +
312
25
+
52
5
)( a + 52 +
52
5
) = 143 a a a + 143 a a ×
52
5
+
44616
5
a ( a +
52
5
) +
267696
25
    The equation is reduced to :
     17500 a a + 182000 a + 1216800( a +
52
5
) + 30000( a + 52 +
312
25
+
52
5
)( a + 52 +
52
5
) = 143 a a a +
7436
5
a a +
44616
5
a ( a +
52
5
) +
267696
25
( a + 52 +
52
5
)
    Remove a bracket on the left of the equation:
     17500 a a + 182000 a + 1216800 a + 1216800 ×
52
5
+ 30000( a + 52 +
312
25
+
52
5
)( a + 52 +
52
5
) = 143 a a a +
7436
5
a a +
44616
5
a ( a +
52
5
) +
267696
25
( a + 52 +
52
5
)
    Remove a bracket on the right of the equation::
     17500 a a + 182000 a + 1216800 a + 1216800 ×
52
5
+ 30000( a + 52 +
312
25
+
52
5
)( a + 52 +
52
5
) = 143 a a a +
7436
5
a a +
44616
5
a a +
44616
5
a
    The equation is reduced to :
     17500 a a + 182000 a + 1216800 a + 12654720 + 30000( a + 52 +
312
25
+
52
5
)( a + 52 +
52
5
) = 143 a a a +
7436
5
a a +
44616
5
a a +
2320032
25
a
    The equation is reduced to :
     17500 a a + 1398800 a + 12654720 + 30000( a + 52 +
312
25
+
52
5
)( a + 52 +
52
5
) = 143 a a a +
7436
5
a a +
44616
5
a a +
2320032
25
a
    Remove a bracket on the left of the equation:
     17500 a a + 1398800 a + 12654720 + 30000 a ( a + 52 +
52
5
) + 30000 × 52( a + 52 +
52
5
) = 143 a a a +
7436
5
a a +
44616
5
a a +
2320032
25
a
    Remove a bracket on the right of the equation::
     17500 a a + 1398800 a + 12654720 + 30000 a ( a + 52 +
52
5
) + 30000 × 52( a + 52 +
52
5
) = 143 a a a +
7436
5
a a +
44616
5
a a +
2320032
25
a
    The equation is reduced to :
     17500 a a + 1398800 a + 12654720 + 30000 a ( a + 52 +
52
5
) + 1560000( a + 52 +
52
5
) + 374400 = 143 a a a +
7436
5
a a +
44616
5
a a +
2320032
25
a
    Remove a bracket on the left of the equation:
     17500 a a + 1398800 a + 12654720 + 30000 a a + 30000 a × 52 = 143 a a a +
7436
5
a a +
44616
5
a a +
2320032
25
a

    The solution of the equation:
        a1≈-70.786532 , keep 6 decimal places
        a2≈-47.585126 , keep 6 decimal places
    
    There are 2 solution(s).


解程的详细方法请参阅:《方程的解法》



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