6a^2+3a-55=0

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Solution for 6a^2+3a-55=0 equation: 


Simplifying
6a2 + 3a + -55 = 0

Reorder the terms:
-55 + 3a + 6a2 = 0

Solving
-55 + 3a + 6a2 = 0

Solving for variable 'a'.

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

Divide each side by '6'.
-9.166666667 + 0.5a + a2 = 0

Move the constant term to the right:

Add '9.166666667' to each side of the equation.
-9.166666667 + 0.5a + 9.166666667 + a2 = 0 + 9.166666667

Reorder the terms:
-9.166666667 + 9.166666667 + 0.5a + a2 = 0 + 9.166666667

Combine like terms: -9.166666667 + 9.166666667 = 0.000000000
0.000000000 + 0.5a + a2 = 0 + 9.166666667
0.5a + a2 = 0 + 9.166666667

Combine like terms: 0 + 9.166666667 = 9.166666667
0.5a + a2 = 9.166666667

The a term is 0.5a.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5a + 0.0625 + a2 = 9.166666667 + 0.0625

Reorder the terms:
0.0625 + 0.5a + a2 = 9.166666667 + 0.0625

Combine like terms: 9.166666667 + 0.0625 = 9.229166667
0.0625 + 0.5a + a2 = 9.229166667

Factor a perfect square on the left side:
(a + 0.25)(a + 0.25) = 9.229166667

Calculate the square root of the right side: 3.037954356

Break this problem into two subproblems by setting 
(a + 0.25) equal to 3.037954356 and -3.037954356.


Subproblem 1
a + 0.25 = 3.037954356

Simplifying
a + 0.25 = 3.037954356

Reorder the terms:
0.25 + a = 3.037954356

Solving
0.25 + a = 3.037954356

Solving for variable 'a'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + a = 3.037954356 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + a = 3.037954356 + -0.25
a = 3.037954356 + -0.25

Combine like terms: 3.037954356 + -0.25 = 2.787954356
a = 2.787954356

Simplifying
a = 2.787954356


Subproblem 2
a + 0.25 = -3.037954356

Simplifying
a + 0.25 = -3.037954356

Reorder the terms:
0.25 + a = -3.037954356

Solving
0.25 + a = -3.037954356

Solving for variable 'a'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + a = -3.037954356 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + a = -3.037954356 + -0.25
a = -3.037954356 + -0.25

Combine like terms: -3.037954356 + -0.25 = -3.287954356
a = -3.287954356

Simplifying
a = -3.287954356


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.787954356, -3.287954356}

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