w^2+3w-27=0

Solution for w^2+3w-27=0 equation:

Simplifying
w2 + 3w + -27 = 0

Reorder the terms:
-27 + 3w + w2 = 0

Solving
-27 + 3w + 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 + 3w + 27 + w2 = 0 + 27

Reorder the terms:
-27 + 27 + 3w + w2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + 3w + w2 = 0 + 27
3w + w2 = 0 + 27

Combine like terms: 0 + 27 = 27
3w + w2 = 27

The w term is 3w.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3w + 2.25 + w2 = 27 + 2.25

Reorder the terms:
2.25 + 3w + w2 = 27 + 2.25

Combine like terms: 27 + 2.25 = 29.25
2.25 + 3w + w2 = 29.25

Factor a perfect square on the left side:
(w + 1.5)(w + 1.5) = 29.25

Calculate the square root of the right side: 5.408326913

Break this problem into two subproblems by setting 
(w + 1.5) equal to 5.408326913 and -5.408326913.

Subproblem 1
w + 1.5 = 5.408326913

Simplifying
w + 1.5 = 5.408326913

Reorder the terms:
1.5 + w = 5.408326913

Solving
1.5 + w = 5.408326913

Solving for variable 'w'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + w = 5.408326913 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = 5.408326913 + -1.5
w = 5.408326913 + -1.5

Combine like terms: 5.408326913 + -1.5 = 3.908326913
w = 3.908326913

Simplifying
w = 3.908326913

Subproblem 2
w + 1.5 = -5.408326913

Simplifying
w + 1.5 = -5.408326913

Reorder the terms:
1.5 + w = -5.408326913

Solving
1.5 + w = -5.408326913

Solving for variable 'w'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + w = -5.408326913 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = -5.408326913 + -1.5
w = -5.408326913 + -1.5

Combine like terms: -5.408326913 + -1.5 = -6.908326913
w = -6.908326913

Simplifying
w = -6.908326913

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {3.908326913, -6.908326913}