2a^2+6a-20=2

Solution for 2a^2+6a-20=2 equation:

Simplifying
2a2 + 6a + -20 = 2

Reorder the terms:
-20 + 6a + 2a2 = 2

Solving
-20 + 6a + 2a2 = 2

Solving for variable 'a'.

Reorder the terms:
-20 + -2 + 6a + 2a2 = 2 + -2

Combine like terms: -20 + -2 = -22
-22 + 6a + 2a2 = 2 + -2

Combine like terms: 2 + -2 = 0
-22 + 6a + 2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-11 + 3a + a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-11 + 3a + a2)' equal to zero and attempt to solve:

Simplifying
-11 + 3a + a2 = 0

Solving
-11 + 3a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 3a + 11 + a2 = 0 + 11

Reorder the terms:
-11 + 11 + 3a + a2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 3a + a2 = 0 + 11
3a + a2 = 0 + 11

Combine like terms: 0 + 11 = 11
3a + a2 = 11

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 = 11 + 2.25

Reorder the terms:
2.25 + 3a + a2 = 11 + 2.25

Combine like terms: 11 + 2.25 = 13.25
2.25 + 3a + a2 = 13.25

Factor a perfect square on the left side:
(a + 1.5)(a + 1.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(a + 1.5) equal to 3.640054945 and -3.640054945.

Subproblem 1
a + 1.5 = 3.640054945

Simplifying
a + 1.5 = 3.640054945

Reorder the terms:
1.5 + a = 3.640054945

Solving
1.5 + a = 3.640054945

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 = 3.640054945 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + a = 3.640054945 + -1.5
a = 3.640054945 + -1.5

Combine like terms: 3.640054945 + -1.5 = 2.140054945
a = 2.140054945

Simplifying
a = 2.140054945

Subproblem 2
a + 1.5 = -3.640054945

Simplifying
a + 1.5 = -3.640054945

Reorder the terms:
1.5 + a = -3.640054945

Solving
1.5 + a = -3.640054945

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 = -3.640054945 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + a = -3.640054945 + -1.5
a = -3.640054945 + -1.5

Combine like terms: -3.640054945 + -1.5 = -5.140054945
a = -5.140054945

Simplifying
a = -5.140054945

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.140054945, -5.140054945}
Solution
a = {2.140054945, -5.140054945}