4k^2-12k+9=12

Solution for 4k^2-12k+9=12 equation:

Simplifying
4k2 + -12k + 9 = 12

Reorder the terms:
9 + -12k + 4k2 = 12

Solving
9 + -12k + 4k2 = 12

Solving for variable 'k'.

Reorder the terms:
9 + -12 + -12k + 4k2 = 12 + -12

Combine like terms: 9 + -12 = -3
-3 + -12k + 4k2 = 12 + -12

Combine like terms: 12 + -12 = 0
-3 + -12k + 4k2 = 0

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

Divide each side by '4'.
-0.75 + -3k + k2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -3k + 0.75 + k2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -3k + k2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -3k + k2 = 0 + 0.75
-3k + k2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-3k + k2 = 0.75

The k term is -3k.  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.
-3k + 2.25 + k2 = 0.75 + 2.25

Reorder the terms:
2.25 + -3k + k2 = 0.75 + 2.25

Combine like terms: 0.75 + 2.25 = 3
2.25 + -3k + k2 = 3

Factor a perfect square on the left side:
(k + -1.5)(k + -1.5) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(k + -1.5) equal to 1.732050808 and -1.732050808.

Subproblem 1
k + -1.5 = 1.732050808

Simplifying
k + -1.5 = 1.732050808

Reorder the terms:
-1.5 + k = 1.732050808

Solving
-1.5 + k = 1.732050808

Solving for variable 'k'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + k = 1.732050808 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + k = 1.732050808 + 1.5
k = 1.732050808 + 1.5

Combine like terms: 1.732050808 + 1.5 = 3.232050808
k = 3.232050808

Simplifying
k = 3.232050808

Subproblem 2
k + -1.5 = -1.732050808

Simplifying
k + -1.5 = -1.732050808

Reorder the terms:
-1.5 + k = -1.732050808

Solving
-1.5 + k = -1.732050808

Solving for variable 'k'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + k = -1.732050808 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + k = -1.732050808 + 1.5
k = -1.732050808 + 1.5

Combine like terms: -1.732050808 + 1.5 = -0.232050808
k = -0.232050808

Simplifying
k = -0.232050808

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {3.232050808, -0.232050808}