5w^2-19w-18=0

Solution for 5w^2-19w-18=0 equation:

Simplifying
5w2 + -19w + -18 = 0

Reorder the terms:
-18 + -19w + 5w2 = 0

Solving
-18 + -19w + 5w2 = 0

Solving for variable 'w'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-3.6 + -3.8w + w2 = 0

Move the constant term to the right:

Add '3.6' to each side of the equation.
-3.6 + -3.8w + 3.6 + w2 = 0 + 3.6

Reorder the terms:
-3.6 + 3.6 + -3.8w + w2 = 0 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + -3.8w + w2 = 0 + 3.6
-3.8w + w2 = 0 + 3.6

Combine like terms: 0 + 3.6 = 3.6
-3.8w + w2 = 3.6

The w term is -3.8w.  Take half its coefficient (-1.9).
Square it (3.61) and add it to both sides.

Add '3.61' to each side of the equation.
-3.8w + 3.61 + w2 = 3.6 + 3.61

Reorder the terms:
3.61 + -3.8w + w2 = 3.6 + 3.61

Combine like terms: 3.6 + 3.61 = 7.21
3.61 + -3.8w + w2 = 7.21

Factor a perfect square on the left side:
(w + -1.9)(w + -1.9) = 7.21

Calculate the square root of the right side: 2.685144316

Break this problem into two subproblems by setting 
(w + -1.9) equal to 2.685144316 and -2.685144316.

Subproblem 1
w + -1.9 = 2.685144316

Simplifying
w + -1.9 = 2.685144316

Reorder the terms:
-1.9 + w = 2.685144316

Solving
-1.9 + w = 2.685144316

Solving for variable 'w'.

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

Add '1.9' to each side of the equation.
-1.9 + 1.9 + w = 2.685144316 + 1.9

Combine like terms: -1.9 + 1.9 = 0.0
0.0 + w = 2.685144316 + 1.9
w = 2.685144316 + 1.9

Combine like terms: 2.685144316 + 1.9 = 4.585144316
w = 4.585144316

Simplifying
w = 4.585144316

Subproblem 2
w + -1.9 = -2.685144316

Simplifying
w + -1.9 = -2.685144316

Reorder the terms:
-1.9 + w = -2.685144316

Solving
-1.9 + w = -2.685144316

Solving for variable 'w'.

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

Add '1.9' to each side of the equation.
-1.9 + 1.9 + w = -2.685144316 + 1.9

Combine like terms: -1.9 + 1.9 = 0.0
0.0 + w = -2.685144316 + 1.9
w = -2.685144316 + 1.9

Combine like terms: -2.685144316 + 1.9 = -0.785144316
w = -0.785144316

Simplifying
w = -0.785144316

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {4.585144316, -0.785144316}