1.2X^2-2X+0.5=0

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Solution for 1.2X^2-2X+0.5=0 equation: 


Simplifying
1.2X2 + -2X + 0.5 = 0

Reorder the terms:
0.5 + -2X + 1.2X2 = 0

Solving
0.5 + -2X + 1.2X2 = 0

Solving for variable 'X'.

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

Divide each side by '1.2'.
0.4166666667 + -1.666666667X + X2 = 0

Move the constant term to the right:

Add '-0.4166666667' to each side of the equation.
0.4166666667 + -1.666666667X + -0.4166666667 + X2 = 0 + -0.4166666667

Reorder the terms:
0.4166666667 + -0.4166666667 + -1.666666667X + X2 = 0 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + -1.666666667X + X2 = 0 + -0.4166666667
-1.666666667X + X2 = 0 + -0.4166666667

Combine like terms: 0 + -0.4166666667 = -0.4166666667
-1.666666667X + X2 = -0.4166666667

The X term is -1.666666667X.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667X + 0.6944444447 + X2 = -0.4166666667 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667X + X2 = -0.4166666667 + 0.6944444447

Combine like terms: -0.4166666667 + 0.6944444447 = 0.277777778
0.6944444447 + -1.666666667X + X2 = 0.277777778

Factor a perfect square on the left side:
(X + -0.8333333335)(X + -0.8333333335) = 0.277777778

Calculate the square root of the right side: 0.527046277

Break this problem into two subproblems by setting 
(X + -0.8333333335) equal to 0.527046277 and -0.527046277.


Subproblem 1
X + -0.8333333335 = 0.527046277

Simplifying
X + -0.8333333335 = 0.527046277

Reorder the terms:
-0.8333333335 + X = 0.527046277

Solving
-0.8333333335 + X = 0.527046277

Solving for variable 'X'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + X = 0.527046277 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + X = 0.527046277 + 0.8333333335
X = 0.527046277 + 0.8333333335

Combine like terms: 0.527046277 + 0.8333333335 = 1.3603796105
X = 1.3603796105

Simplifying
X = 1.3603796105


Subproblem 2
X + -0.8333333335 = -0.527046277

Simplifying
X + -0.8333333335 = -0.527046277

Reorder the terms:
-0.8333333335 + X = -0.527046277

Solving
-0.8333333335 + X = -0.527046277

Solving for variable 'X'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + X = -0.527046277 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + X = -0.527046277 + 0.8333333335
X = -0.527046277 + 0.8333333335

Combine like terms: -0.527046277 + 0.8333333335 = 0.3062870565
X = 0.3062870565

Simplifying
X = 0.3062870565


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {1.3603796105, 0.3062870565}

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