0.06X^2-0.8X+1.96=0

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Solution for 0.06X^2-0.8X+1.96=0 equation: 


Simplifying
0.06X2 + -0.8X + 1.96 = 0

Reorder the terms:
1.96 + -0.8X + 0.06X2 = 0

Solving
1.96 + -0.8X + 0.06X2 = 0

Solving for variable 'X'.

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

Divide each side by '0.06'.
32.66666667 + -13.33333333X + X2 = 0

Move the constant term to the right:

Add '-32.66666667' to each side of the equation.
32.66666667 + -13.33333333X + -32.66666667 + X2 = 0 + -32.66666667

Reorder the terms:
32.66666667 + -32.66666667 + -13.33333333X + X2 = 0 + -32.66666667

Combine like terms: 32.66666667 + -32.66666667 = 0.00000000
0.00000000 + -13.33333333X + X2 = 0 + -32.66666667
-13.33333333X + X2 = 0 + -32.66666667

Combine like terms: 0 + -32.66666667 = -32.66666667
-13.33333333X + X2 = -32.66666667

The X term is -13.33333333X.  Take half its coefficient (-6.666666665).
Square it (44.44444442) and add it to both sides.

Add '44.44444442' to each side of the equation.
-13.33333333X + 44.44444442 + X2 = -32.66666667 + 44.44444442

Reorder the terms:
44.44444442 + -13.33333333X + X2 = -32.66666667 + 44.44444442

Combine like terms: -32.66666667 + 44.44444442 = 11.77777775
44.44444442 + -13.33333333X + X2 = 11.77777775

Factor a perfect square on the left side:
(X + -6.666666665)(X + -6.666666665) = 11.77777775

Calculate the square root of the right side: 3.43187671

Break this problem into two subproblems by setting 
(X + -6.666666665) equal to 3.43187671 and -3.43187671.


Subproblem 1
X + -6.666666665 = 3.43187671

Simplifying
X + -6.666666665 = 3.43187671

Reorder the terms:
-6.666666665 + X = 3.43187671

Solving
-6.666666665 + X = 3.43187671

Solving for variable 'X'.

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

Add '6.666666665' to each side of the equation.
-6.666666665 + 6.666666665 + X = 3.43187671 + 6.666666665

Combine like terms: -6.666666665 + 6.666666665 = 0.000000000
0.000000000 + X = 3.43187671 + 6.666666665
X = 3.43187671 + 6.666666665

Combine like terms: 3.43187671 + 6.666666665 = 10.098543375
X = 10.098543375

Simplifying
X = 10.098543375


Subproblem 2
X + -6.666666665 = -3.43187671

Simplifying
X + -6.666666665 = -3.43187671

Reorder the terms:
-6.666666665 + X = -3.43187671

Solving
-6.666666665 + X = -3.43187671

Solving for variable 'X'.

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

Add '6.666666665' to each side of the equation.
-6.666666665 + 6.666666665 + X = -3.43187671 + 6.666666665

Combine like terms: -6.666666665 + 6.666666665 = 0.000000000
0.000000000 + X = -3.43187671 + 6.666666665
X = -3.43187671 + 6.666666665

Combine like terms: -3.43187671 + 6.666666665 = 3.234789955
X = 3.234789955

Simplifying
X = 3.234789955


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {10.098543375, 3.234789955}

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