137.87*X*(137.87*X+694.55)=44.7135811*(137.87*X+694.55)

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Solution for 137.87*X*(137.87*X+694.55)=44.7135811*(137.87*X+694.55) equation: 


Simplifying
137.87X(137.87X + 694.55) = 44.7135811(137.87X + 694.55)

Reorder the terms:
137.87X(694.55 + 137.87X) = 44.7135811(137.87X + 694.55)
(694.55 * 137.87X + 137.87X * 137.87X) = 44.7135811(137.87X + 694.55)
(95757.6085X + 19008.1369X2) = 44.7135811(137.87X + 694.55)

Reorder the terms:
95757.6085X + 19008.1369X2 = 44.7135811(694.55 + 137.87X)
95757.6085X + 19008.1369X2 = (694.55 * 44.7135811 + 137.87X * 44.7135811)
95757.6085X + 19008.1369X2 = (31055.81775 + 6164.661426X)

Solving
95757.6085X + 19008.1369X2 = 31055.81775 + 6164.661426X

Solving for variable 'X'.

Reorder the terms:
-31055.81775 + 95757.6085X + -6164.661426X + 19008.1369X2 = 31055.81775 + 6164.661426X + -31055.81775 + -6164.661426X

Combine like terms: 95757.6085X + -6164.661426X = 89592.947074X
-31055.81775 + 89592.947074X + 19008.1369X2 = 31055.81775 + 6164.661426X + -31055.81775 + -6164.661426X

Reorder the terms:
-31055.81775 + 89592.947074X + 19008.1369X2 = 31055.81775 + -31055.81775 + 6164.661426X + -6164.661426X

Combine like terms: 31055.81775 + -31055.81775 = 0.00000
-31055.81775 + 89592.947074X + 19008.1369X2 = 0.00000 + 6164.661426X + -6164.661426X
-31055.81775 + 89592.947074X + 19008.1369X2 = 6164.661426X + -6164.661426X

Combine like terms: 6164.661426X + -6164.661426X = 0.000000
-31055.81775 + 89592.947074X + 19008.1369X2 = 0.000000

Begin completing the square.  Divide all terms by
19008.1369 the coefficient of the squared term: 

Divide each side by '19008.1369'.
-1.633817029 + 4.713399716X + X2 = 0.00

Move the constant term to the right:

Add '1.633817029' to each side of the equation.
-1.633817029 + 4.713399716X + 1.633817029 + X2 = 0.00 + 1.633817029

Reorder the terms:
-1.633817029 + 1.633817029 + 4.713399716X + X2 = 0.00 + 1.633817029

Combine like terms: -1.633817029 + 1.633817029 = 0.000000000
0.000000000 + 4.713399716X + X2 = 0.00 + 1.633817029
4.713399716X + X2 = 0.00 + 1.633817029

Combine like terms: 0.00 + 1.633817029 = 1.633817029
4.713399716X + X2 = 1.633817029

The X term is 4.713399716X.  Take half its coefficient (2.356699858).
Square it (5.554034221) and add it to both sides.

Add '5.554034221' to each side of the equation.
4.713399716X + 5.554034221 + X2 = 1.633817029 + 5.554034221

Reorder the terms:
5.554034221 + 4.713399716X + X2 = 1.633817029 + 5.554034221

Combine like terms: 1.633817029 + 5.554034221 = 7.18785125
5.554034221 + 4.713399716X + X2 = 7.18785125

Factor a perfect square on the left side:
(X + 2.356699858)(X + 2.356699858) = 7.18785125

Calculate the square root of the right side: 2.681016831

Break this problem into two subproblems by setting 
(X + 2.356699858) equal to 2.681016831 and -2.681016831.


Subproblem 1
X + 2.356699858 = 2.681016831

Simplifying
X + 2.356699858 = 2.681016831

Reorder the terms:
2.356699858 + X = 2.681016831

Solving
2.356699858 + X = 2.681016831

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

Add '-2.356699858' to each side of the equation.
2.356699858 + -2.356699858 + X = 2.681016831 + -2.356699858

Combine like terms: 2.356699858 + -2.356699858 = 0.000000000
0.000000000 + X = 2.681016831 + -2.356699858
X = 2.681016831 + -2.356699858

Combine like terms: 2.681016831 + -2.356699858 = 0.324316973
X = 0.324316973

Simplifying
X = 0.324316973


Subproblem 2
X + 2.356699858 = -2.681016831

Simplifying
X + 2.356699858 = -2.681016831

Reorder the terms:
2.356699858 + X = -2.681016831

Solving
2.356699858 + X = -2.681016831

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

Add '-2.356699858' to each side of the equation.
2.356699858 + -2.356699858 + X = -2.681016831 + -2.356699858

Combine like terms: 2.356699858 + -2.356699858 = 0.000000000
0.000000000 + X = -2.681016831 + -2.356699858
X = -2.681016831 + -2.356699858

Combine like terms: -2.681016831 + -2.356699858 = -5.037716689
X = -5.037716689

Simplifying
X = -5.037716689


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.324316973, -5.037716689}

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