3.6x^2+2.1x-3.9=0

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Solution for 3.6x^2+2.1x-3.9=0 equation: 


Simplifying
3.6x2 + 2.1x + -3.9 = 0

Reorder the terms:
-3.9 + 2.1x + 3.6x2 = 0

Solving
-3.9 + 2.1x + 3.6x2 = 0

Solving for variable 'x'.

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

Divide each side by '3.6'.
-1.083333333 + 0.5833333333x + x2 = 0

Move the constant term to the right:

Add '1.083333333' to each side of the equation.
-1.083333333 + 0.5833333333x + 1.083333333 + x2 = 0 + 1.083333333

Reorder the terms:
-1.083333333 + 1.083333333 + 0.5833333333x + x2 = 0 + 1.083333333

Combine like terms: -1.083333333 + 1.083333333 = 0.000000000
0.000000000 + 0.5833333333x + x2 = 0 + 1.083333333
0.5833333333x + x2 = 0 + 1.083333333

Combine like terms: 0 + 1.083333333 = 1.083333333
0.5833333333x + x2 = 1.083333333

The x term is 0.5833333333x.  Take half its coefficient (0.2916666667).
Square it (0.08506944446) and add it to both sides.

Add '0.08506944446' to each side of the equation.
0.5833333333x + 0.08506944446 + x2 = 1.083333333 + 0.08506944446

Reorder the terms:
0.08506944446 + 0.5833333333x + x2 = 1.083333333 + 0.08506944446

Combine like terms: 1.083333333 + 0.08506944446 = 1.16840277746
0.08506944446 + 0.5833333333x + x2 = 1.16840277746

Factor a perfect square on the left side:
(x + 0.2916666667)(x + 0.2916666667) = 1.16840277746

Calculate the square root of the right side: 1.080926814

Break this problem into two subproblems by setting 
(x + 0.2916666667) equal to 1.080926814 and -1.080926814.


Subproblem 1
x + 0.2916666667 = 1.080926814

Simplifying
x + 0.2916666667 = 1.080926814

Reorder the terms:
0.2916666667 + x = 1.080926814

Solving
0.2916666667 + x = 1.080926814

Solving for variable 'x'.

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

Add '-0.2916666667' to each side of the equation.
0.2916666667 + -0.2916666667 + x = 1.080926814 + -0.2916666667

Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000
0.0000000000 + x = 1.080926814 + -0.2916666667
x = 1.080926814 + -0.2916666667

Combine like terms: 1.080926814 + -0.2916666667 = 0.7892601473
x = 0.7892601473

Simplifying
x = 0.7892601473


Subproblem 2
x + 0.2916666667 = -1.080926814

Simplifying
x + 0.2916666667 = -1.080926814

Reorder the terms:
0.2916666667 + x = -1.080926814

Solving
0.2916666667 + x = -1.080926814

Solving for variable 'x'.

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

Add '-0.2916666667' to each side of the equation.
0.2916666667 + -0.2916666667 + x = -1.080926814 + -0.2916666667

Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000
0.0000000000 + x = -1.080926814 + -0.2916666667
x = -1.080926814 + -0.2916666667

Combine like terms: -1.080926814 + -0.2916666667 = -1.3725934807
x = -1.3725934807

Simplifying
x = -1.3725934807


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.7892601473, -1.3725934807}

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