a-2=a^2-6

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

Simplifying
a + -2 = a2 + -6

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

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

Solving
-2 + a = -6 + a2

Solving for variable 'a'.

Reorder the terms:
-2 + 6 + a + -1a2 = -6 + a2 + 6 + -1a2

Combine like terms: -2 + 6 = 4
4 + a + -1a2 = -6 + a2 + 6 + -1a2

Reorder the terms:
4 + a + -1a2 = -6 + 6 + a2 + -1a2

Combine like terms: -6 + 6 = 0
4 + a + -1a2 = 0 + a2 + -1a2
4 + a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
4 + a + -1a2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-4 + -1a + a2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -1a + 4 + a2 = 0 + 4

Reorder the terms:
-4 + 4 + -1a + a2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1a + a2 = 0 + 4
-1a + a2 = 0 + 4

Combine like terms: 0 + 4 = 4
-1a + a2 = 4

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.
-1a + 0.25 + a2 = 4 + 0.25

Reorder the terms:
0.25 + -1a + a2 = 4 + 0.25

Combine like terms: 4 + 0.25 = 4.25
0.25 + -1a + a2 = 4.25

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(a + 0.5) equal to 2.061552813 and -2.061552813.

Subproblem 1
a + 0.5 = 2.061552813

Simplifying
a + 0.5 = 2.061552813

Reorder the terms:
0.5 + a = 2.061552813

Solving
0.5 + a = 2.061552813

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 = 2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = 2.061552813 + -0.5
a = 2.061552813 + -0.5

Combine like terms: 2.061552813 + -0.5 = 1.561552813
a = 1.561552813

Simplifying
a = 1.561552813

Subproblem 2
a + 0.5 = -2.061552813

Simplifying
a + 0.5 = -2.061552813

Reorder the terms:
0.5 + a = -2.061552813

Solving
0.5 + a = -2.061552813

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 = -2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = -2.061552813 + -0.5
a = -2.061552813 + -0.5

Combine like terms: -2.061552813 + -0.5 = -2.561552813
a = -2.561552813

Simplifying
a = -2.561552813

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.561552813, -2.561552813}