2a^2+2a-16=0

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


Simplifying
2a2 + 2a + -16 = 0

Reorder the terms:
-16 + 2a + 2a2 = 0

Solving
-16 + 2a + 2a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + a + a2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + a + a2)' equal to zero and attempt to solve:

Simplifying
-8 + a + a2 = 0

Solving
-8 + a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + a + 8 + a2 = 0 + 8

Reorder the terms:
-8 + 8 + a + a2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + a + a2 = 0 + 8
a + a2 = 0 + 8

Combine like terms: 0 + 8 = 8
a + a2 = 8

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 = 8 + 0.25

Reorder the terms:
0.25 + a + a2 = 8 + 0.25

Combine like terms: 8 + 0.25 = 8.25
0.25 + a + a2 = 8.25

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(a + 0.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
a + 0.5 = 2.872281323

Simplifying
a + 0.5 = 2.872281323

Reorder the terms:
0.5 + a = 2.872281323

Solving
0.5 + a = 2.872281323

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 = 2.872281323 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = 2.872281323 + -0.5
a = 2.872281323 + -0.5

Combine like terms: 2.872281323 + -0.5 = 2.372281323
a = 2.372281323

Simplifying
a = 2.372281323


Subproblem 2
a + 0.5 = -2.872281323

Simplifying
a + 0.5 = -2.872281323

Reorder the terms:
0.5 + a = -2.872281323

Solving
0.5 + a = -2.872281323

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 = -2.872281323 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = -2.872281323 + -0.5
a = -2.872281323 + -0.5

Combine like terms: -2.872281323 + -0.5 = -3.372281323
a = -3.372281323

Simplifying
a = -3.372281323


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.372281323, -3.372281323}
Solution
a = {2.372281323, -3.372281323}

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