w^2-8w-27=0

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Solution for w^2-8w-27=0 equation: 


Simplifying
w2 + -8w + -27 = 0

Reorder the terms:
-27 + -8w + w2 = 0

Solving
-27 + -8w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + -8w + 27 + w2 = 0 + 27

Reorder the terms:
-27 + 27 + -8w + w2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -8w + w2 = 0 + 27
-8w + w2 = 0 + 27

Combine like terms: 0 + 27 = 27
-8w + w2 = 27

The w term is -8w.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8w + 16 + w2 = 27 + 16

Reorder the terms:
16 + -8w + w2 = 27 + 16

Combine like terms: 27 + 16 = 43
16 + -8w + w2 = 43

Factor a perfect square on the left side:
(w + -4)(w + -4) = 43

Calculate the square root of the right side: 6.557438524

Break this problem into two subproblems by setting 
(w + -4) equal to 6.557438524 and -6.557438524.


Subproblem 1
w + -4 = 6.557438524

Simplifying
w + -4 = 6.557438524

Reorder the terms:
-4 + w = 6.557438524

Solving
-4 + w = 6.557438524

Solving for variable 'w'.

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

Add '4' to each side of the equation.
-4 + 4 + w = 6.557438524 + 4

Combine like terms: -4 + 4 = 0
0 + w = 6.557438524 + 4
w = 6.557438524 + 4

Combine like terms: 6.557438524 + 4 = 10.557438524
w = 10.557438524

Simplifying
w = 10.557438524


Subproblem 2
w + -4 = -6.557438524

Simplifying
w + -4 = -6.557438524

Reorder the terms:
-4 + w = -6.557438524

Solving
-4 + w = -6.557438524

Solving for variable 'w'.

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

Add '4' to each side of the equation.
-4 + 4 + w = -6.557438524 + 4

Combine like terms: -4 + 4 = 0
0 + w = -6.557438524 + 4
w = -6.557438524 + 4

Combine like terms: -6.557438524 + 4 = -2.557438524
w = -2.557438524

Simplifying
w = -2.557438524


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {10.557438524, -2.557438524}

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