w^2-13w+42.25=0

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

Simplifying
w2 + -13w + 42.25 = 0

Reorder the terms:
42.25 + -13w + w2 = 0

Solving
42.25 + -13w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '-42.25' to each side of the equation.
42.25 + -13w + -42.25 + w2 = 0 + -42.25

Reorder the terms:
42.25 + -42.25 + -13w + w2 = 0 + -42.25

Combine like terms: 42.25 + -42.25 = 0.00
0.00 + -13w + w2 = 0 + -42.25
-13w + w2 = 0 + -42.25

Combine like terms: 0 + -42.25 = -42.25
-13w + w2 = -42.25

The w term is -13w.  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.
-13w + 42.25 + w2 = -42.25 + 42.25

Reorder the terms:
42.25 + -13w + w2 = -42.25 + 42.25

Combine like terms: -42.25 + 42.25 = 0.00
42.25 + -13w + w2 = 0.00

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

Calculate the square root of the right side: 0.00

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

Subproblem 1
w + -6.5 = 0.00

Simplifying
w + -6.5 = 0.00

Reorder the terms:
-6.5 + w = 0.00

Solving
-6.5 + w = 0.00

Solving for variable 'w'.

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

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

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

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

Simplifying
w = 6.5

Subproblem 2
w + -6.5 = 0.00

Simplifying
w + -6.5 = 0.00

Reorder the terms:
-6.5 + w = 0.00

Solving
-6.5 + w = 0.00

Solving for variable 'w'.

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

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

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

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

Simplifying
w = 6.5

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