2*(a^2+4a-4)=

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Solution for 2*(a^2+4a-4)= equation: 


Simplifying
2(a2 + 4a + -4) = 0

Reorder the terms:
2(-4 + 4a + a2) = 0
(-4 * 2 + 4a * 2 + a2 * 2) = 0
(-8 + 8a + 2a2) = 0

Solving
-8 + 8a + 2a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 4a + a2) = 0

Ignore the factor 2.

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 = 0.828427125
a = 0.828427125

Simplifying
a = 0.828427125


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 = -4.828427125
a = -4.828427125

Simplifying
a = -4.828427125


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

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