x^2-12.5x+36=0

Solution for x^2-12.5x+36=0 equation:

Simplifying
x2 + -12.5x + 36 = 0

Reorder the terms:
36 + -12.5x + x2 = 0

Solving
36 + -12.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + -12.5x + -36 + x2 = 0 + -36

Reorder the terms:
36 + -36 + -12.5x + x2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -12.5x + x2 = 0 + -36
-12.5x + x2 = 0 + -36

Combine like terms: 0 + -36 = -36
-12.5x + x2 = -36

The x term is -12.5x.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5x + 39.0625 + x2 = -36 + 39.0625

Reorder the terms:
39.0625 + -12.5x + x2 = -36 + 39.0625

Combine like terms: -36 + 39.0625 = 3.0625
39.0625 + -12.5x + x2 = 3.0625

Factor a perfect square on the left side:
(x + -6.25)(x + -6.25) = 3.0625

Calculate the square root of the right side: 1.75

Break this problem into two subproblems by setting 
(x + -6.25) equal to 1.75 and -1.75.

Subproblem 1
x + -6.25 = 1.75

Simplifying
x + -6.25 = 1.75

Reorder the terms:
-6.25 + x = 1.75

Solving
-6.25 + x = 1.75

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = 1.75 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = 1.75 + 6.25
x = 1.75 + 6.25

Combine like terms: 1.75 + 6.25 = 8
x = 8

Simplifying
x = 8

Subproblem 2
x + -6.25 = -1.75

Simplifying
x + -6.25 = -1.75

Reorder the terms:
-6.25 + x = -1.75

Solving
-6.25 + x = -1.75

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = -1.75 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = -1.75 + 6.25
x = -1.75 + 6.25

Combine like terms: -1.75 + 6.25 = 4.5
x = 4.5

Simplifying
x = 4.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8, 4.5}