w^2-27w+40=0

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Solution for w^2-27w+40=0 equation: 


Simplifying
w2 + -27w + 40 = 0

Reorder the terms:
40 + -27w + w2 = 0

Solving
40 + -27w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + -27w + -40 + w2 = 0 + -40

Reorder the terms:
40 + -40 + -27w + w2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -27w + w2 = 0 + -40
-27w + w2 = 0 + -40

Combine like terms: 0 + -40 = -40
-27w + w2 = -40

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 = -40 + 182.25

Reorder the terms:
182.25 + -27w + w2 = -40 + 182.25

Combine like terms: -40 + 182.25 = 142.25
182.25 + -27w + w2 = 142.25

Factor a perfect square on the left side:
(w + -13.5)(w + -13.5) = 142.25

Calculate the square root of the right side: 11.926860442

Break this problem into two subproblems by setting 
(w + -13.5) equal to 11.926860442 and -11.926860442.


Subproblem 1
w + -13.5 = 11.926860442

Simplifying
w + -13.5 = 11.926860442

Reorder the terms:
-13.5 + w = 11.926860442

Solving
-13.5 + w = 11.926860442

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 = 11.926860442 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + w = 11.926860442 + 13.5
w = 11.926860442 + 13.5

Combine like terms: 11.926860442 + 13.5 = 25.426860442
w = 25.426860442

Simplifying
w = 25.426860442


Subproblem 2
w + -13.5 = -11.926860442

Simplifying
w + -13.5 = -11.926860442

Reorder the terms:
-13.5 + w = -11.926860442

Solving
-13.5 + w = -11.926860442

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 = -11.926860442 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + w = -11.926860442 + 13.5
w = -11.926860442 + 13.5

Combine like terms: -11.926860442 + 13.5 = 1.573139558
w = 1.573139558

Simplifying
w = 1.573139558


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {25.426860442, 1.573139558}

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