w^2+w-48=0

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Solution for w^2+w-48=0 equation: 


Simplifying
w2 + w + -48 = 0

Reorder the terms:
-48 + w + w2 = 0

Solving
-48 + w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + w + 48 + w2 = 0 + 48

Reorder the terms:
-48 + 48 + w + w2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + w + w2 = 0 + 48
w + w2 = 0 + 48

Combine like terms: 0 + 48 = 48
w + w2 = 48

The w term is w.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
w + 0.25 + w2 = 48 + 0.25

Reorder the terms:
0.25 + w + w2 = 48 + 0.25

Combine like terms: 48 + 0.25 = 48.25
0.25 + w + w2 = 48.25

Factor a perfect square on the left side:
(w + 0.5)(w + 0.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(w + 0.5) equal to 6.946221995 and -6.946221995.


Subproblem 1
w + 0.5 = 6.946221995

Simplifying
w + 0.5 = 6.946221995

Reorder the terms:
0.5 + w = 6.946221995

Solving
0.5 + w = 6.946221995

Solving for variable 'w'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + w = 6.946221995 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = 6.946221995 + -0.5
w = 6.946221995 + -0.5

Combine like terms: 6.946221995 + -0.5 = 6.446221995
w = 6.446221995

Simplifying
w = 6.446221995


Subproblem 2
w + 0.5 = -6.946221995

Simplifying
w + 0.5 = -6.946221995

Reorder the terms:
0.5 + w = -6.946221995

Solving
0.5 + w = -6.946221995

Solving for variable 'w'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + w = -6.946221995 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = -6.946221995 + -0.5
w = -6.946221995 + -0.5

Combine like terms: -6.946221995 + -0.5 = -7.446221995
w = -7.446221995

Simplifying
w = -7.446221995


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {6.446221995, -7.446221995}

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