w^2-27w-72=0

Solution for w^2-27w-72=0 equation:

Simplifying
w2 + -27w + -72 = 0

Reorder the terms:
-72 + -27w + w2 = 0

Solving
-72 + -27w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + -27w + 72 + w2 = 0 + 72

Reorder the terms:
-72 + 72 + -27w + w2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + -27w + w2 = 0 + 72
-27w + w2 = 0 + 72

Combine like terms: 0 + 72 = 72
-27w + w2 = 72

The w term is -27w.  Take half its coefficient (-13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
-27w + 182.25 + w2 = 72 + 182.25

Reorder the terms:
182.25 + -27w + w2 = 72 + 182.25

Combine like terms: 72 + 182.25 = 254.25
182.25 + -27w + w2 = 254.25

Factor a perfect square on the left side:
(w + -13.5)(w + -13.5) = 254.25

Calculate the square root of the right side: 15.945218719

Break this problem into two subproblems by setting 
(w + -13.5) equal to 15.945218719 and -15.945218719.

Subproblem 1
w + -13.5 = 15.945218719

Simplifying
w + -13.5 = 15.945218719

Reorder the terms:
-13.5 + w = 15.945218719

Solving
-13.5 + w = 15.945218719

Solving for variable 'w'.

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

Add '13.5' to each side of the equation.
-13.5 + 13.5 + w = 15.945218719 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + w = 15.945218719 + 13.5
w = 15.945218719 + 13.5

Combine like terms: 15.945218719 + 13.5 = 29.445218719
w = 29.445218719

Simplifying
w = 29.445218719

Subproblem 2
w + -13.5 = -15.945218719

Simplifying
w + -13.5 = -15.945218719

Reorder the terms:
-13.5 + w = -15.945218719

Solving
-13.5 + w = -15.945218719

Solving for variable 'w'.

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

Add '13.5' to each side of the equation.
-13.5 + 13.5 + w = -15.945218719 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + w = -15.945218719 + 13.5
w = -15.945218719 + 13.5

Combine like terms: -15.945218719 + 13.5 = -2.445218719
w = -2.445218719

Simplifying
w = -2.445218719

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {29.445218719, -2.445218719}