137.87*X*(137.87*X+694.55)=0.447135811*(137.87*X+694.55)

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Solution for 137.87*X*(137.87*X+694.55)=0.447135811*(137.87*X+694.55) equation:


Simplifying
137.87X(137.87X + 694.55) = 0.447135811(137.87X + 694.55)

Reorder the terms:
137.87X(694.55 + 137.87X) = 0.447135811(137.87X + 694.55)
(694.55 * 137.87X + 137.87X * 137.87X) = 0.447135811(137.87X + 694.55)
(95757.6085X + 19008.1369X2) = 0.447135811(137.87X + 694.55)

Reorder the terms:
95757.6085X + 19008.1369X2 = 0.447135811(694.55 + 137.87X)
95757.6085X + 19008.1369X2 = (694.55 * 0.447135811 + 137.87X * 0.447135811)
95757.6085X + 19008.1369X2 = (310.5581775 + 61.64661426X)

Solving
95757.6085X + 19008.1369X2 = 310.5581775 + 61.64661426X

Solving for variable 'X'.

Reorder the terms:
-310.5581775 + 95757.6085X + -61.64661426X + 19008.1369X2 = 310.5581775 + 61.64661426X + -310.5581775 + -61.64661426X

Combine like terms: 95757.6085X + -61.64661426X = 95695.96188574X
-310.5581775 + 95695.96188574X + 19008.1369X2 = 310.5581775 + 61.64661426X + -310.5581775 + -61.64661426X

Reorder the terms:
-310.5581775 + 95695.96188574X + 19008.1369X2 = 310.5581775 + -310.5581775 + 61.64661426X + -61.64661426X

Combine like terms: 310.5581775 + -310.5581775 = 0.0000000
-310.5581775 + 95695.96188574X + 19008.1369X2 = 0.0000000 + 61.64661426X + -61.64661426X
-310.5581775 + 95695.96188574X + 19008.1369X2 = 61.64661426X + -61.64661426X

Combine like terms: 61.64661426X + -61.64661426X = 0.00000000
-310.5581775 + 95695.96188574X + 19008.1369X2 = 0.00000000

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

Divide each side by '19008.1369'.
-0.01633817029 + 5.03447352X + X2 = 0.0000

Move the constant term to the right:

Add '0.01633817029' to each side of the equation.
-0.01633817029 + 5.03447352X + 0.01633817029 + X2 = 0.0000 + 0.01633817029

Reorder the terms:
-0.01633817029 + 0.01633817029 + 5.03447352X + X2 = 0.0000 + 0.01633817029

Combine like terms: -0.01633817029 + 0.01633817029 = 0.00000000000
0.00000000000 + 5.03447352X + X2 = 0.0000 + 0.01633817029
5.03447352X + X2 = 0.0000 + 0.01633817029

Combine like terms: 0.0000 + 0.01633817029 = 0.01633817029
5.03447352X + X2 = 0.01633817029

The X term is 5.03447352X.  Take half its coefficient (2.51723676).
Square it (6.336480906) and add it to both sides.

Add '6.336480906' to each side of the equation.
5.03447352X + 6.336480906 + X2 = 0.01633817029 + 6.336480906

Reorder the terms:
6.336480906 + 5.03447352X + X2 = 0.01633817029 + 6.336480906

Combine like terms: 0.01633817029 + 6.336480906 = 6.35281907629
6.336480906 + 5.03447352X + X2 = 6.35281907629

Factor a perfect square on the left side:
(X + 2.51723676)(X + 2.51723676) = 6.35281907629

Calculate the square root of the right side: 2.52047993

Break this problem into two subproblems by setting 
(X + 2.51723676) equal to 2.52047993 and -2.52047993.

Subproblem 1

X + 2.51723676 = 2.52047993 Simplifying X + 2.51723676 = 2.52047993 Reorder the terms: 2.51723676 + X = 2.52047993 Solving 2.51723676 + X = 2.52047993 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.51723676' to each side of the equation. 2.51723676 + -2.51723676 + X = 2.52047993 + -2.51723676 Combine like terms: 2.51723676 + -2.51723676 = 0.00000000 0.00000000 + X = 2.52047993 + -2.51723676 X = 2.52047993 + -2.51723676 Combine like terms: 2.52047993 + -2.51723676 = 0.00324317 X = 0.00324317 Simplifying X = 0.00324317

Subproblem 2

X + 2.51723676 = -2.52047993 Simplifying X + 2.51723676 = -2.52047993 Reorder the terms: 2.51723676 + X = -2.52047993 Solving 2.51723676 + X = -2.52047993 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.51723676' to each side of the equation. 2.51723676 + -2.51723676 + X = -2.52047993 + -2.51723676 Combine like terms: 2.51723676 + -2.51723676 = 0.00000000 0.00000000 + X = -2.52047993 + -2.51723676 X = -2.52047993 + -2.51723676 Combine like terms: -2.52047993 + -2.51723676 = -5.03771669 X = -5.03771669 Simplifying X = -5.03771669

Solution

The solution to the problem is based on the solutions from the subproblems. X = {0.00324317, -5.03771669}

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