5w^2+4w-548=0

Solution for 5w^2+4w-548=0 equation:

Simplifying
5w2 + 4w + -548 = 0

Reorder the terms:
-548 + 4w + 5w2 = 0

Solving
-548 + 4w + 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'.
-109.6 + 0.8w + w2 = 0

Move the constant term to the right:

Add '109.6' to each side of the equation.
-109.6 + 0.8w + 109.6 + w2 = 0 + 109.6

Reorder the terms:
-109.6 + 109.6 + 0.8w + w2 = 0 + 109.6

Combine like terms: -109.6 + 109.6 = 0.0
0.0 + 0.8w + w2 = 0 + 109.6
0.8w + w2 = 0 + 109.6

Combine like terms: 0 + 109.6 = 109.6
0.8w + w2 = 109.6

The w term is 0.8w.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8w + 0.16 + w2 = 109.6 + 0.16

Reorder the terms:
0.16 + 0.8w + w2 = 109.6 + 0.16

Combine like terms: 109.6 + 0.16 = 109.76
0.16 + 0.8w + w2 = 109.76

Factor a perfect square on the left side:
(w + 0.4)(w + 0.4) = 109.76

Calculate the square root of the right side: 10.476640683

Break this problem into two subproblems by setting 
(w + 0.4) equal to 10.476640683 and -10.476640683.

Subproblem 1
w + 0.4 = 10.476640683

Simplifying
w + 0.4 = 10.476640683

Reorder the terms:
0.4 + w = 10.476640683

Solving
0.4 + w = 10.476640683

Solving for variable 'w'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + w = 10.476640683 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + w = 10.476640683 + -0.4
w = 10.476640683 + -0.4

Combine like terms: 10.476640683 + -0.4 = 10.076640683
w = 10.076640683

Simplifying
w = 10.076640683

Subproblem 2
w + 0.4 = -10.476640683

Simplifying
w + 0.4 = -10.476640683

Reorder the terms:
0.4 + w = -10.476640683

Solving
0.4 + w = -10.476640683

Solving for variable 'w'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + w = -10.476640683 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + w = -10.476640683 + -0.4
w = -10.476640683 + -0.4

Combine like terms: -10.476640683 + -0.4 = -10.876640683
w = -10.876640683

Simplifying
w = -10.876640683

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {10.076640683, -10.876640683}