0.25x^2-6x+36=0

Solution for 0.25x^2-6x+36=0 equation:

Simplifying
0.25x2 + -6x + 36 = 0

Reorder the terms:
36 + -6x + 0.25x2 = 0

Solving
36 + -6x + 0.25x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.25'.
144 + -24x + x2 = 0

Move the constant term to the right:

Add '-144' to each side of the equation.
144 + -24x + -144 + x2 = 0 + -144

Reorder the terms:
144 + -144 + -24x + x2 = 0 + -144

Combine like terms: 144 + -144 = 0
0 + -24x + x2 = 0 + -144
-24x + x2 = 0 + -144

Combine like terms: 0 + -144 = -144
-24x + x2 = -144

The x term is -24x.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24x + 144 + x2 = -144 + 144

Reorder the terms:
144 + -24x + x2 = -144 + 144

Combine like terms: -144 + 144 = 0
144 + -24x + x2 = 0

Factor a perfect square on the left side:
(x + -12)(x + -12) = 0

Calculate the square root of the right side: 0

Break this problem into two subproblems by setting 
(x + -12) equal to 0 and 0.

Subproblem 1
x + -12 = 0

Simplifying
x + -12 = 0

Reorder the terms:
-12 + x = 0

Solving
-12 + x = 0

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + x = 0 + 12
x = 0 + 12

Combine like terms: 0 + 12 = 12
x = 12

Simplifying
x = 12

Subproblem 2
x + -12 = 0

Simplifying
x + -12 = 0

Reorder the terms:
-12 + x = 0

Solving
-12 + x = 0

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + x = 0 + 12
x = 0 + 12

Combine like terms: 0 + 12 = 12
x = 12

Simplifying
x = 12

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12, 12}