2a^2-6a-27=

Solution for 2a^2-6a-27= equation:

Simplifying
2a2 + -6a + -27 = 0

Reorder the terms:
-27 + -6a + 2a2 = 0

Solving
-27 + -6a + 2a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-13.5 + -3a + a2 = 0

Move the constant term to the right:

Add '13.5' to each side of the equation.
-13.5 + -3a + 13.5 + a2 = 0 + 13.5

Reorder the terms:
-13.5 + 13.5 + -3a + a2 = 0 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + -3a + a2 = 0 + 13.5
-3a + a2 = 0 + 13.5

Combine like terms: 0 + 13.5 = 13.5
-3a + a2 = 13.5

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 = 13.5 + 2.25

Reorder the terms:
2.25 + -3a + a2 = 13.5 + 2.25

Combine like terms: 13.5 + 2.25 = 15.75
2.25 + -3a + a2 = 15.75

Factor a perfect square on the left side:
(a + -1.5)(a + -1.5) = 15.75

Calculate the square root of the right side: 3.968626967

Break this problem into two subproblems by setting 
(a + -1.5) equal to 3.968626967 and -3.968626967.

Subproblem 1
a + -1.5 = 3.968626967

Simplifying
a + -1.5 = 3.968626967

Reorder the terms:
-1.5 + a = 3.968626967

Solving
-1.5 + a = 3.968626967

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 = 3.968626967 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + a = 3.968626967 + 1.5
a = 3.968626967 + 1.5

Combine like terms: 3.968626967 + 1.5 = 5.468626967
a = 5.468626967

Simplifying
a = 5.468626967

Subproblem 2
a + -1.5 = -3.968626967

Simplifying
a + -1.5 = -3.968626967

Reorder the terms:
-1.5 + a = -3.968626967

Solving
-1.5 + a = -3.968626967

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 = -3.968626967 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + a = -3.968626967 + 1.5
a = -3.968626967 + 1.5

Combine like terms: -3.968626967 + 1.5 = -2.468626967
a = -2.468626967

Simplifying
a = -2.468626967

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {5.468626967, -2.468626967}