w^2+5w-240=0

Solution for w^2+5w-240=0 equation:

Simplifying
w2 + 5w + -240 = 0

Reorder the terms:
-240 + 5w + w2 = 0

Solving
-240 + 5w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '240' to each side of the equation.
-240 + 5w + 240 + w2 = 0 + 240

Reorder the terms:
-240 + 240 + 5w + w2 = 0 + 240

Combine like terms: -240 + 240 = 0
0 + 5w + w2 = 0 + 240
5w + w2 = 0 + 240

Combine like terms: 0 + 240 = 240
5w + w2 = 240

The w term is 5w.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5w + 6.25 + w2 = 240 + 6.25

Reorder the terms:
6.25 + 5w + w2 = 240 + 6.25

Combine like terms: 240 + 6.25 = 246.25
6.25 + 5w + w2 = 246.25

Factor a perfect square on the left side:
(w + 2.5)(w + 2.5) = 246.25

Calculate the square root of the right side: 15.692354826

Break this problem into two subproblems by setting 
(w + 2.5) equal to 15.692354826 and -15.692354826.

Subproblem 1
w + 2.5 = 15.692354826

Simplifying
w + 2.5 = 15.692354826

Reorder the terms:
2.5 + w = 15.692354826

Solving
2.5 + w = 15.692354826

Solving for variable 'w'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + w = 15.692354826 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = 15.692354826 + -2.5
w = 15.692354826 + -2.5

Combine like terms: 15.692354826 + -2.5 = 13.192354826
w = 13.192354826

Simplifying
w = 13.192354826

Subproblem 2
w + 2.5 = -15.692354826

Simplifying
w + 2.5 = -15.692354826

Reorder the terms:
2.5 + w = -15.692354826

Solving
2.5 + w = -15.692354826

Solving for variable 'w'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + w = -15.692354826 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = -15.692354826 + -2.5
w = -15.692354826 + -2.5

Combine like terms: -15.692354826 + -2.5 = -18.192354826
w = -18.192354826

Simplifying
w = -18.192354826

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {13.192354826, -18.192354826}