18a^2-6a+0.5=0

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Solution for 18a^2-6a+0.5=0 equation: 


Simplifying
18a2 + -6a + 0.5 = 0

Reorder the terms:
0.5 + -6a + 18a2 = 0

Solving
0.5 + -6a + 18a2 = 0

Solving for variable 'a'.

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

Divide each side by '18'.
0.02777777778 + -0.3333333333a + a2 = 0

Move the constant term to the right:

Add '-0.02777777778' to each side of the equation.
0.02777777778 + -0.3333333333a + -0.02777777778 + a2 = 0 + -0.02777777778

Reorder the terms:
0.02777777778 + -0.02777777778 + -0.3333333333a + a2 = 0 + -0.02777777778

Combine like terms: 0.02777777778 + -0.02777777778 = 0.00000000000
0.00000000000 + -0.3333333333a + a2 = 0 + -0.02777777778
-0.3333333333a + a2 = 0 + -0.02777777778

Combine like terms: 0 + -0.02777777778 = -0.02777777778
-0.3333333333a + a2 = -0.02777777778

The a term is -0.3333333333a.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333a + 0.02777777779 + a2 = -0.02777777778 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333a + a2 = -0.02777777778 + 0.02777777779

Combine like terms: -0.02777777778 + 0.02777777779 = 0.00000000001
0.02777777779 + -0.3333333333a + a2 = 0.00000000001

Factor a perfect square on the left side:
(a + -0.1666666667)(a + -0.1666666667) = 0.00000000001

Calculate the square root of the right side: 0.000003162

Break this problem into two subproblems by setting 
(a + -0.1666666667) equal to 0.000003162 and -0.000003162.


Subproblem 1
a + -0.1666666667 = 0.000003162

Simplifying
a + -0.1666666667 = 0.000003162

Reorder the terms:
-0.1666666667 + a = 0.000003162

Solving
-0.1666666667 + a = 0.000003162

Solving for variable 'a'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + a = 0.000003162 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + a = 0.000003162 + 0.1666666667
a = 0.000003162 + 0.1666666667

Combine like terms: 0.000003162 + 0.1666666667 = 0.1666698287
a = 0.1666698287

Simplifying
a = 0.1666698287


Subproblem 2
a + -0.1666666667 = -0.000003162

Simplifying
a + -0.1666666667 = -0.000003162

Reorder the terms:
-0.1666666667 + a = -0.000003162

Solving
-0.1666666667 + a = -0.000003162

Solving for variable 'a'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + a = -0.000003162 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + a = -0.000003162 + 0.1666666667
a = -0.000003162 + 0.1666666667

Combine like terms: -0.000003162 + 0.1666666667 = 0.1666635047
a = 0.1666635047

Simplifying
a = 0.1666635047


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.1666698287, 0.1666635047}

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