0.0416666a^2+0.25a+0.33333333=0

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Solution for 0.0416666a^2+0.25a+0.33333333=0 equation: 


Simplifying
0.0416666a2 + 0.25a + 0.33333333 = 0

Reorder the terms:
0.33333333 + 0.25a + 0.0416666a2 = 0

Solving
0.33333333 + 0.25a + 0.0416666a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
0.0416666 the coefficient of the squared term: 

Divide each side by '0.0416666'.
8.00001272 + 6.0000096a + a2 = 0

Move the constant term to the right:

Add '-8.00001272' to each side of the equation.
8.00001272 + 6.0000096a + -8.00001272 + a2 = 0 + -8.00001272

Reorder the terms:
8.00001272 + -8.00001272 + 6.0000096a + a2 = 0 + -8.00001272

Combine like terms: 8.00001272 + -8.00001272 = 0.00000000
0.00000000 + 6.0000096a + a2 = 0 + -8.00001272
6.0000096a + a2 = 0 + -8.00001272

Combine like terms: 0 + -8.00001272 = -8.00001272
6.0000096a + a2 = -8.00001272

The a term is 6.0000096a.  Take half its coefficient (3.0000048).
Square it (9.000028800) and add it to both sides.

Add '9.000028800' to each side of the equation.
6.0000096a + 9.000028800 + a2 = -8.00001272 + 9.000028800

Reorder the terms:
9.000028800 + 6.0000096a + a2 = -8.00001272 + 9.000028800

Combine like terms: -8.00001272 + 9.000028800 = 1.00001608
9.000028800 + 6.0000096a + a2 = 1.00001608

Factor a perfect square on the left side:
(a + 3.0000048)(a + 3.0000048) = 1.00001608

Calculate the square root of the right side: 1.00000804

Break this problem into two subproblems by setting 
(a + 3.0000048) equal to 1.00000804 and -1.00000804.


Subproblem 1
a + 3.0000048 = 1.00000804

Simplifying
a + 3.0000048 = 1.00000804

Reorder the terms:
3.0000048 + a = 1.00000804

Solving
3.0000048 + a = 1.00000804

Solving for variable 'a'.

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

Add '-3.0000048' to each side of the equation.
3.0000048 + -3.0000048 + a = 1.00000804 + -3.0000048

Combine like terms: 3.0000048 + -3.0000048 = 0.0000000
0.0000000 + a = 1.00000804 + -3.0000048
a = 1.00000804 + -3.0000048

Combine like terms: 1.00000804 + -3.0000048 = -1.99999676
a = -1.99999676

Simplifying
a = -1.99999676


Subproblem 2
a + 3.0000048 = -1.00000804

Simplifying
a + 3.0000048 = -1.00000804

Reorder the terms:
3.0000048 + a = -1.00000804

Solving
3.0000048 + a = -1.00000804

Solving for variable 'a'.

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

Add '-3.0000048' to each side of the equation.
3.0000048 + -3.0000048 + a = -1.00000804 + -3.0000048

Combine like terms: 3.0000048 + -3.0000048 = 0.0000000
0.0000000 + a = -1.00000804 + -3.0000048
a = -1.00000804 + -3.0000048

Combine like terms: -1.00000804 + -3.0000048 = -4.00001284
a = -4.00001284

Simplifying
a = -4.00001284


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-1.99999676, -4.00001284}

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