4a^2-16a-16=0

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Solution for 4a^2-16a-16=0 equation: 


Simplifying
4a2 + -16a + -16 = 0

Reorder the terms:
-16 + -16a + 4a2 = 0

Solving
-16 + -16a + 4a2 = 0

Solving for variable 'a'.

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

Ignore the factor 4.

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

Simplifying
-4 + -4a + a2 = 0

Solving
-4 + -4a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -4a + 4 + a2 = 0 + 4

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

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

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

The a term is -4a.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4a + 4 + a2 = 4 + 4

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

Combine like terms: 4 + 4 = 8
4 + -4a + a2 = 8

Factor a perfect square on the left side:
(a + -2)(a + -2) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(a + -2) equal to 2.828427125 and -2.828427125.


Subproblem 1
a + -2 = 2.828427125

Simplifying
a + -2 = 2.828427125

Reorder the terms:
-2 + a = 2.828427125

Solving
-2 + a = 2.828427125

Solving for variable 'a'.

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

Add '2' to each side of the equation.
-2 + 2 + a = 2.828427125 + 2

Combine like terms: -2 + 2 = 0
0 + a = 2.828427125 + 2
a = 2.828427125 + 2

Combine like terms: 2.828427125 + 2 = 4.828427125
a = 4.828427125

Simplifying
a = 4.828427125


Subproblem 2
a + -2 = -2.828427125

Simplifying
a + -2 = -2.828427125

Reorder the terms:
-2 + a = -2.828427125

Solving
-2 + a = -2.828427125

Solving for variable 'a'.

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

Add '2' to each side of the equation.
-2 + 2 + a = -2.828427125 + 2

Combine like terms: -2 + 2 = 0
0 + a = -2.828427125 + 2
a = -2.828427125 + 2

Combine like terms: -2.828427125 + 2 = -0.828427125
a = -0.828427125

Simplifying
a = -0.828427125


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {4.828427125, -0.828427125}
Solution
a = {4.828427125, -0.828427125}

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