a^2-2+27a=0

Solution for a^2-2+27a=0 equation:

Simplifying
a2 + -2 + 27a = 0

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

Solving
-2 + 27a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 27a + 2 + a2 = 0 + 2

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

Combine like terms: -2 + 2 = 0
0 + 27a + a2 = 0 + 2
27a + a2 = 0 + 2

Combine like terms: 0 + 2 = 2
27a + a2 = 2

The a term is 27a.  Take half its coefficient (13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
27a + 182.25 + a2 = 2 + 182.25

Reorder the terms:
182.25 + 27a + a2 = 2 + 182.25

Combine like terms: 2 + 182.25 = 184.25
182.25 + 27a + a2 = 184.25

Factor a perfect square on the left side:
(a + 13.5)(a + 13.5) = 184.25

Calculate the square root of the right side: 13.57387196

Break this problem into two subproblems by setting 
(a + 13.5) equal to 13.57387196 and -13.57387196.

Subproblem 1
a + 13.5 = 13.57387196

Simplifying
a + 13.5 = 13.57387196

Reorder the terms:
13.5 + a = 13.57387196

Solving
13.5 + a = 13.57387196

Solving for variable 'a'.

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

Add '-13.5' to each side of the equation.
13.5 + -13.5 + a = 13.57387196 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + a = 13.57387196 + -13.5
a = 13.57387196 + -13.5

Combine like terms: 13.57387196 + -13.5 = 0.07387196
a = 0.07387196

Simplifying
a = 0.07387196

Subproblem 2
a + 13.5 = -13.57387196

Simplifying
a + 13.5 = -13.57387196

Reorder the terms:
13.5 + a = -13.57387196

Solving
13.5 + a = -13.57387196

Solving for variable 'a'.

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

Add '-13.5' to each side of the equation.
13.5 + -13.5 + a = -13.57387196 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + a = -13.57387196 + -13.5
a = -13.57387196 + -13.5

Combine like terms: -13.57387196 + -13.5 = -27.07387196
a = -27.07387196

Simplifying
a = -27.07387196

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.07387196, -27.07387196}