=a^2-12a+3

Solution for =a^2-12a+3 equation:

Simplifying
0 = a2 + -12a + 3

Reorder the terms:
0 = 3 + -12a + a2

Solving
0 = 3 + -12a + a2

Solving for variable 'a'.

Combine like terms: 0 + -3 = -3
-3 + 12a + -1a2 = 3 + -12a + a2 + -3 + 12a + -1a2

Reorder the terms:
-3 + 12a + -1a2 = 3 + -3 + -12a + 12a + a2 + -1a2

Combine like terms: 3 + -3 = 0
-3 + 12a + -1a2 = 0 + -12a + 12a + a2 + -1a2
-3 + 12a + -1a2 = -12a + 12a + a2 + -1a2

Combine like terms: -12a + 12a = 0
-3 + 12a + -1a2 = 0 + a2 + -1a2
-3 + 12a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-3 + 12a + -1a2 = 0

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

Divide each side by '-1'.
3 + -12a + a2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -12a + -3 + a2 = 0 + -3

Reorder the terms:
3 + -3 + -12a + a2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -12a + a2 = 0 + -3
-12a + a2 = 0 + -3

Combine like terms: 0 + -3 = -3
-12a + a2 = -3

The a term is -12a.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12a + 36 + a2 = -3 + 36

Reorder the terms:
36 + -12a + a2 = -3 + 36

Combine like terms: -3 + 36 = 33
36 + -12a + a2 = 33

Factor a perfect square on the left side:
(a + -6)(a + -6) = 33

Calculate the square root of the right side: 5.744562647

Break this problem into two subproblems by setting 
(a + -6) equal to 5.744562647 and -5.744562647.

Subproblem 1
a + -6 = 5.744562647

Simplifying
a + -6 = 5.744562647

Reorder the terms:
-6 + a = 5.744562647

Solving
-6 + a = 5.744562647

Solving for variable 'a'.

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

Add '6' to each side of the equation.
-6 + 6 + a = 5.744562647 + 6

Combine like terms: -6 + 6 = 0
0 + a = 5.744562647 + 6
a = 5.744562647 + 6

Combine like terms: 5.744562647 + 6 = 11.744562647
a = 11.744562647

Simplifying
a = 11.744562647

Subproblem 2
a + -6 = -5.744562647

Simplifying
a + -6 = -5.744562647

Reorder the terms:
-6 + a = -5.744562647

Solving
-6 + a = -5.744562647

Solving for variable 'a'.

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

Add '6' to each side of the equation.
-6 + 6 + a = -5.744562647 + 6

Combine like terms: -6 + 6 = 0
0 + a = -5.744562647 + 6
a = -5.744562647 + 6

Combine like terms: -5.744562647 + 6 = 0.255437353
a = 0.255437353

Simplifying
a = 0.255437353

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {11.744562647, 0.255437353}