2(a+1+a^2)=64

Solution for 2(a+1+a^2)=64 equation:

Simplifying
2(a + 1 + a2) = 64

Reorder the terms:
2(1 + a + a2) = 64
(1 * 2 + a * 2 + a2 * 2) = 64
(2 + 2a + 2a2) = 64

Solving
2 + 2a + 2a2 = 64

Solving for variable 'a'.

Reorder the terms:
2 + -64 + 2a + 2a2 = 64 + -64

Combine like terms: 2 + -64 = -62
-62 + 2a + 2a2 = 64 + -64

Combine like terms: 64 + -64 = 0
-62 + 2a + 2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-31 + a + a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-31 + a + a2)' equal to zero and attempt to solve:

Simplifying
-31 + a + a2 = 0

Solving
-31 + a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + a + 31 + a2 = 0 + 31

Reorder the terms:
-31 + 31 + a + a2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + a + a2 = 0 + 31
a + a2 = 0 + 31

Combine like terms: 0 + 31 = 31
a + a2 = 31

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.
a + 0.25 + a2 = 31 + 0.25

Reorder the terms:
0.25 + a + a2 = 31 + 0.25

Combine like terms: 31 + 0.25 = 31.25
0.25 + a + a2 = 31.25

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = 31.25

Calculate the square root of the right side: 5.590169944

Break this problem into two subproblems by setting 
(a + 0.5) equal to 5.590169944 and -5.590169944.

Subproblem 1
a + 0.5 = 5.590169944

Simplifying
a + 0.5 = 5.590169944

Reorder the terms:
0.5 + a = 5.590169944

Solving
0.5 + a = 5.590169944

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 = 5.590169944 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = 5.590169944 + -0.5
a = 5.590169944 + -0.5

Combine like terms: 5.590169944 + -0.5 = 5.090169944
a = 5.090169944

Simplifying
a = 5.090169944

Subproblem 2
a + 0.5 = -5.590169944

Simplifying
a + 0.5 = -5.590169944

Reorder the terms:
0.5 + a = -5.590169944

Solving
0.5 + a = -5.590169944

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 = -5.590169944 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = -5.590169944 + -0.5
a = -5.590169944 + -0.5

Combine like terms: -5.590169944 + -0.5 = -6.090169944
a = -6.090169944

Simplifying
a = -6.090169944

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {5.090169944, -6.090169944}
Solution
a = {5.090169944, -6.090169944}