2a^2+6a-8=2

Solution for 2a^2+6a-8=2 equation:

Simplifying
2a2 + 6a + -8 = 2

Reorder the terms:
-8 + 6a + 2a2 = 2

Solving
-8 + 6a + 2a2 = 2

Solving for variable 'a'.

Reorder the terms:
-8 + -2 + 6a + 2a2 = 2 + -2

Combine like terms: -8 + -2 = -10
-10 + 6a + 2a2 = 2 + -2

Combine like terms: 2 + -2 = 0
-10 + 6a + 2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 3a + a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + 3a + a2)' equal to zero and attempt to solve:

Simplifying
-5 + 3a + a2 = 0

Solving
-5 + 3a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 3a + 5 + a2 = 0 + 5

Reorder the terms:
-5 + 5 + 3a + a2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 3a + a2 = 0 + 5
3a + a2 = 0 + 5

Combine like terms: 0 + 5 = 5
3a + a2 = 5

The a term is 3a.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3a + 2.25 + a2 = 5 + 2.25

Reorder the terms:
2.25 + 3a + a2 = 5 + 2.25

Combine like terms: 5 + 2.25 = 7.25
2.25 + 3a + a2 = 7.25

Factor a perfect square on the left side:
(a + 1.5)(a + 1.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(a + 1.5) equal to 2.692582404 and -2.692582404.

Subproblem 1
a + 1.5 = 2.692582404

Simplifying
a + 1.5 = 2.692582404

Reorder the terms:
1.5 + a = 2.692582404

Solving
1.5 + a = 2.692582404

Solving for variable 'a'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + a = 2.692582404 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + a = 2.692582404 + -1.5
a = 2.692582404 + -1.5

Combine like terms: 2.692582404 + -1.5 = 1.192582404
a = 1.192582404

Simplifying
a = 1.192582404

Subproblem 2
a + 1.5 = -2.692582404

Simplifying
a + 1.5 = -2.692582404

Reorder the terms:
1.5 + a = -2.692582404

Solving
1.5 + a = -2.692582404

Solving for variable 'a'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + a = -2.692582404 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + a = -2.692582404 + -1.5
a = -2.692582404 + -1.5

Combine like terms: -2.692582404 + -1.5 = -4.192582404
a = -4.192582404

Simplifying
a = -4.192582404

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.192582404, -4.192582404}
Solution
a = {1.192582404, -4.192582404}