0=x^2-13x+42.25

Solution for 0=x^2-13x+42.25 equation:

Simplifying
0 = x2 + -13x + 42.25

Reorder the terms:
0 = 42.25 + -13x + x2

Solving
0 = 42.25 + -13x + x2

Solving for variable 'x'.

Combine like terms: 0 + -42.25 = -42.25
-42.25 + 13x + -1x2 = 42.25 + -13x + x2 + -42.25 + 13x + -1x2

Reorder the terms:
-42.25 + 13x + -1x2 = 42.25 + -42.25 + -13x + 13x + x2 + -1x2

Combine like terms: 42.25 + -42.25 = 0.00
-42.25 + 13x + -1x2 = 0.00 + -13x + 13x + x2 + -1x2
-42.25 + 13x + -1x2 = -13x + 13x + x2 + -1x2

Combine like terms: -13x + 13x = 0
-42.25 + 13x + -1x2 = 0 + x2 + -1x2
-42.25 + 13x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-42.25 + 13x + -1x2 = 0

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

Divide each side by '-1'.
42.25 + -13x + x2 = 0

Move the constant term to the right:

Add '-42.25' to each side of the equation.
42.25 + -13x + -42.25 + x2 = 0 + -42.25

Reorder the terms:
42.25 + -42.25 + -13x + x2 = 0 + -42.25

Combine like terms: 42.25 + -42.25 = 0.00
0.00 + -13x + x2 = 0 + -42.25
-13x + x2 = 0 + -42.25

Combine like terms: 0 + -42.25 = -42.25
-13x + x2 = -42.25

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = -42.25 + 42.25

Reorder the terms:
42.25 + -13x + x2 = -42.25 + 42.25

Combine like terms: -42.25 + 42.25 = 0.00
42.25 + -13x + x2 = 0.00

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(x + -6.5) equal to 0.00 and 0.00.

Subproblem 1
x + -6.5 = 0.00

Simplifying
x + -6.5 = 0.00

Reorder the terms:
-6.5 + x = 0.00

Solving
-6.5 + x = 0.00

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = 0.00 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 0.00 + 6.5
x = 0.00 + 6.5

Combine like terms: 0.00 + 6.5 = 6.5
x = 6.5

Simplifying
x = 6.5

Subproblem 2
x + -6.5 = 0.00

Simplifying
x + -6.5 = 0.00

Reorder the terms:
-6.5 + x = 0.00

Solving
-6.5 + x = 0.00

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = 0.00 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 0.00 + 6.5
x = 0.00 + 6.5

Combine like terms: 0.00 + 6.5 = 6.5
x = 6.5

Simplifying
x = 6.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.5, 6.5}