0=w^2+5w-42

Solution for 0=w^2+5w-42 equation:

Simplifying
0 = w2 + 5w + -42

Reorder the terms:
0 = -42 + 5w + w2

Solving
0 = -42 + 5w + w2

Solving for variable 'w'.

Combine like terms: 0 + 42 = 42
42 + -5w + -1w2 = -42 + 5w + w2 + 42 + -5w + -1w2

Reorder the terms:
42 + -5w + -1w2 = -42 + 42 + 5w + -5w + w2 + -1w2

Combine like terms: -42 + 42 = 0
42 + -5w + -1w2 = 0 + 5w + -5w + w2 + -1w2
42 + -5w + -1w2 = 5w + -5w + w2 + -1w2

Combine like terms: 5w + -5w = 0
42 + -5w + -1w2 = 0 + w2 + -1w2
42 + -5w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
42 + -5w + -1w2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-42 + 5w + w2 = 0

Move the constant term to the right:

Add '42' to each side of the equation.
-42 + 5w + 42 + w2 = 0 + 42

Reorder the terms:
-42 + 42 + 5w + w2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + 5w + w2 = 0 + 42
5w + w2 = 0 + 42

Combine like terms: 0 + 42 = 42
5w + w2 = 42

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 = 42 + 6.25

Reorder the terms:
6.25 + 5w + w2 = 42 + 6.25

Combine like terms: 42 + 6.25 = 48.25
6.25 + 5w + w2 = 48.25

Factor a perfect square on the left side:
(w + 2.5)(w + 2.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(w + 2.5) equal to 6.946221995 and -6.946221995.

Subproblem 1
w + 2.5 = 6.946221995

Simplifying
w + 2.5 = 6.946221995

Reorder the terms:
2.5 + w = 6.946221995

Solving
2.5 + w = 6.946221995

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 = 6.946221995 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = 6.946221995 + -2.5
w = 6.946221995 + -2.5

Combine like terms: 6.946221995 + -2.5 = 4.446221995
w = 4.446221995

Simplifying
w = 4.446221995

Subproblem 2
w + 2.5 = -6.946221995

Simplifying
w + 2.5 = -6.946221995

Reorder the terms:
2.5 + w = -6.946221995

Solving
2.5 + w = -6.946221995

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 = -6.946221995 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = -6.946221995 + -2.5
w = -6.946221995 + -2.5

Combine like terms: -6.946221995 + -2.5 = -9.446221995
w = -9.446221995

Simplifying
w = -9.446221995

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {4.446221995, -9.446221995}