2X(3X+4)-19=X(6X-2)31

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Solution for 2X(3X+4)-19=X(6X-2)31 equation: 


Simplifying
2X(3X + 4) + -19 = X(6X + -2) * 31

Reorder the terms:
2X(4 + 3X) + -19 = X(6X + -2) * 31
(4 * 2X + 3X * 2X) + -19 = X(6X + -2) * 31
(8X + 6X2) + -19 = X(6X + -2) * 31

Reorder the terms:
-19 + 8X + 6X2 = X(6X + -2) * 31

Reorder the terms:
-19 + 8X + 6X2 = X(-2 + 6X) * 31

Reorder the terms for easier multiplication:
-19 + 8X + 6X2 = 31X(-2 + 6X)
-19 + 8X + 6X2 = (-2 * 31X + 6X * 31X)
-19 + 8X + 6X2 = (-62X + 186X2)

Solving
-19 + 8X + 6X2 = -62X + 186X2

Solving for variable 'X'.

Reorder the terms:
-19 + 8X + 62X + 6X2 + -186X2 = -62X + 186X2 + 62X + -186X2

Combine like terms: 8X + 62X = 70X
-19 + 70X + 6X2 + -186X2 = -62X + 186X2 + 62X + -186X2

Combine like terms: 6X2 + -186X2 = -180X2
-19 + 70X + -180X2 = -62X + 186X2 + 62X + -186X2

Reorder the terms:
-19 + 70X + -180X2 = -62X + 62X + 186X2 + -186X2

Combine like terms: -62X + 62X = 0
-19 + 70X + -180X2 = 0 + 186X2 + -186X2
-19 + 70X + -180X2 = 186X2 + -186X2

Combine like terms: 186X2 + -186X2 = 0
-19 + 70X + -180X2 = 0

Begin completing the square.  Divide all terms by
-180 the coefficient of the squared term: 

Divide each side by '-180'.
0.1055555556 + -0.3888888889X + X2 = 0.0

Move the constant term to the right:

Add '-0.1055555556' to each side of the equation.
0.1055555556 + -0.3888888889X + -0.1055555556 + X2 = 0.0 + -0.1055555556

Reorder the terms:
0.1055555556 + -0.1055555556 + -0.3888888889X + X2 = 0.0 + -0.1055555556

Combine like terms: 0.1055555556 + -0.1055555556 = 0.0000000000
0.0000000000 + -0.3888888889X + X2 = 0.0 + -0.1055555556
-0.3888888889X + X2 = 0.0 + -0.1055555556

Combine like terms: 0.0 + -0.1055555556 = -0.1055555556
-0.3888888889X + X2 = -0.1055555556

The X term is -0.3888888889X.  Take half its coefficient (-0.1944444445).
Square it (0.03780864200) and add it to both sides.

Add '0.03780864200' to each side of the equation.
-0.3888888889X + 0.03780864200 + X2 = -0.1055555556 + 0.03780864200

Reorder the terms:
0.03780864200 + -0.3888888889X + X2 = -0.1055555556 + 0.03780864200

Combine like terms: -0.1055555556 + 0.03780864200 = -0.0677469136
0.03780864200 + -0.3888888889X + X2 = -0.0677469136

Factor a perfect square on the left side:
(X + -0.1944444445)(X + -0.1944444445) = -0.0677469136

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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