4a-66a*65744(-555)a=16

Solution for 4a-66a*65744(-555)a=16 equation:

Simplifying
4a + -66a * 65744(-555) * a = 16

Reorder the terms for easier multiplication:
4a + -66 * 65744 * -555a * a = 16

Multiply -66 * 65744
4a + -4339104 * -555a * a = 16

Multiply -4339104 * -555
4a + 2408202720a * a = 16

Multiply a * a
4a + 2408202720a2 = 16

Solving
4a + 2408202720a2 = 16

Solving for variable 'a'.

Reorder the terms:
-16 + 4a + 2408202720a2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 4a + 2408202720a2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + a + 602050680a2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-4 + a + 602050680a2)' equal to zero and attempt to solve:

Simplifying
-4 + a + 602050680a2 = 0

Solving
-4 + a + 602050680a2 = 0

Begin completing the square.  Divide all terms by
602050680 the coefficient of the squared term: 

Divide each side by '602050680'.
-0.000000006643958944 + 0.000000001660989736a + a2 = 0.0

Move the constant term to the right:

Add '0.000000006643958944' to each side of the equation.
-0.000000006643958944 + 0.000000001660989736a + 0.000000006643958944 + a2 = 0.0 + 0.000000006643958944

Reorder the terms:
-0.000000006643958944 + 0.000000006643958944 + 0.000000001660989736a + a2 = 0.0 + 0.000000006643958944

Combine like terms: -0.000000006643958944 + 0.000000006643958944 = 0.000000000000000000
0.000000000000000000 + 0.000000001660989736a + a2 = 0.0 + 0.000000006643958944
0.000000001660989736a + a2 = 0.0 + 0.000000006643958944

Combine like terms: 0.0 + 0.000000006643958944 = 0.000000006643958944
0.000000001660989736a + a2 = 0.000000006643958944

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

Add '0.25' to each side of the equation.
0.000000001660989736a + 0.25 + a2 = 0.000000006643958944 + 0.25

Reorder the terms:
0.25 + 0.000000001660989736a + a2 = 0.000000006643958944 + 0.25

Combine like terms: 0.000000006643958944 + 0.25 = 0.250000006643958944
0.25 + 0.000000001660989736a + a2 = 0.250000006643958944

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = 0.250000006643958944

Calculate the square root of the right side: 0.500000007

Break this problem into two subproblems by setting 
(a + 0.5) equal to 0.500000007 and -0.500000007.

Subproblem 1
a + 0.5 = 0.500000007

Simplifying
a + 0.5 = 0.500000007

Reorder the terms:
0.5 + a = 0.500000007

Solving
0.5 + a = 0.500000007

Solving for variable 'a'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + a = 0.500000007 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = 0.500000007 + -0.5
a = 0.500000007 + -0.5

Combine like terms: 0.500000007 + -0.5 = 0.000000007
a = 0.000000007

Simplifying
a = 0.000000007

Subproblem 2
a + 0.5 = -0.500000007

Simplifying
a + 0.5 = -0.500000007

Reorder the terms:
0.5 + a = -0.500000007

Solving
0.5 + a = -0.500000007

Solving for variable 'a'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + a = -0.500000007 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = -0.500000007 + -0.5
a = -0.500000007 + -0.5

Combine like terms: -0.500000007 + -0.5 = -1.000000007
a = -1.000000007

Simplifying
a = -1.000000007

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.000000007, -1.000000007}
Solution
a = {0.000000007, -1.000000007}