4a^2-4a-256=0

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Solution for 4a^2-4a-256=0 equation: 


Simplifying
4a2 + -4a + -256 = 0

Reorder the terms:
-256 + -4a + 4a2 = 0

Solving
-256 + -4a + 4a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-64 + -1a + a2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-64 + -1a + a2)' equal to zero and attempt to solve:

Simplifying
-64 + -1a + a2 = 0

Solving
-64 + -1a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + -1a + 64 + a2 = 0 + 64

Reorder the terms:
-64 + 64 + -1a + a2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + -1a + a2 = 0 + 64
-1a + a2 = 0 + 64

Combine like terms: 0 + 64 = 64
-1a + a2 = 64

The a term is -1a.  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.
-1a + 0.25 + a2 = 64 + 0.25

Reorder the terms:
0.25 + -1a + a2 = 64 + 0.25

Combine like terms: 64 + 0.25 = 64.25
0.25 + -1a + a2 = 64.25

Factor a perfect square on the left side:
(a + -0.5)(a + -0.5) = 64.25

Calculate the square root of the right side: 8.015609771

Break this problem into two subproblems by setting 
(a + -0.5) equal to 8.015609771 and -8.015609771.


Subproblem 1
a + -0.5 = 8.015609771

Simplifying
a + -0.5 = 8.015609771

Reorder the terms:
-0.5 + a = 8.015609771

Solving
-0.5 + a = 8.015609771

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 = 8.015609771 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + a = 8.015609771 + 0.5
a = 8.015609771 + 0.5

Combine like terms: 8.015609771 + 0.5 = 8.515609771
a = 8.515609771

Simplifying
a = 8.515609771


Subproblem 2
a + -0.5 = -8.015609771

Simplifying
a + -0.5 = -8.015609771

Reorder the terms:
-0.5 + a = -8.015609771

Solving
-0.5 + a = -8.015609771

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 = -8.015609771 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + a = -8.015609771 + 0.5
a = -8.015609771 + 0.5

Combine like terms: -8.015609771 + 0.5 = -7.515609771
a = -7.515609771

Simplifying
a = -7.515609771


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {8.515609771, -7.515609771}
Solution
a = {8.515609771, -7.515609771}

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