k^2-3=3k

Solution for k^2-3=3k equation:

Simplifying
k2 + -3 = 3k

Reorder the terms:
-3 + k2 = 3k

Solving
-3 + k2 = 3k

Solving for variable 'k'.

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 3 + 2.25

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

Combine like terms: 3 + 2.25 = 5.25
2.25 + -3k + k2 = 5.25

Factor a perfect square on the left side:
(k + -1.5)(k + -1.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(k + -1.5) equal to 2.291287847 and -2.291287847.

Subproblem 1
k + -1.5 = 2.291287847

Simplifying
k + -1.5 = 2.291287847

Reorder the terms:
-1.5 + k = 2.291287847

Solving
-1.5 + k = 2.291287847

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 = 2.291287847 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + k = 2.291287847 + 1.5
k = 2.291287847 + 1.5

Combine like terms: 2.291287847 + 1.5 = 3.791287847
k = 3.791287847

Simplifying
k = 3.791287847

Subproblem 2
k + -1.5 = -2.291287847

Simplifying
k + -1.5 = -2.291287847

Reorder the terms:
-1.5 + k = -2.291287847

Solving
-1.5 + k = -2.291287847

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 = -2.291287847 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + k = -2.291287847 + 1.5
k = -2.291287847 + 1.5

Combine like terms: -2.291287847 + 1.5 = -0.791287847
k = -0.791287847

Simplifying
k = -0.791287847

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {3.791287847, -0.791287847}