w^2-3w-220=0

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Solution for w^2-3w-220=0 equation: 


Simplifying
w2 + -3w + -220 = 0

Reorder the terms:
-220 + -3w + w2 = 0

Solving
-220 + -3w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '220' to each side of the equation.
-220 + -3w + 220 + w2 = 0 + 220

Reorder the terms:
-220 + 220 + -3w + w2 = 0 + 220

Combine like terms: -220 + 220 = 0
0 + -3w + w2 = 0 + 220
-3w + w2 = 0 + 220

Combine like terms: 0 + 220 = 220
-3w + w2 = 220

The w term is -3w.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3w + 2.25 + w2 = 220 + 2.25

Reorder the terms:
2.25 + -3w + w2 = 220 + 2.25

Combine like terms: 220 + 2.25 = 222.25
2.25 + -3w + w2 = 222.25

Factor a perfect square on the left side:
(w + -1.5)(w + -1.5) = 222.25

Calculate the square root of the right side: 14.908051516

Break this problem into two subproblems by setting 
(w + -1.5) equal to 14.908051516 and -14.908051516.


Subproblem 1
w + -1.5 = 14.908051516

Simplifying
w + -1.5 = 14.908051516

Reorder the terms:
-1.5 + w = 14.908051516

Solving
-1.5 + w = 14.908051516

Solving for variable 'w'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + w = 14.908051516 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + w = 14.908051516 + 1.5
w = 14.908051516 + 1.5

Combine like terms: 14.908051516 + 1.5 = 16.408051516
w = 16.408051516

Simplifying
w = 16.408051516


Subproblem 2
w + -1.5 = -14.908051516

Simplifying
w + -1.5 = -14.908051516

Reorder the terms:
-1.5 + w = -14.908051516

Solving
-1.5 + w = -14.908051516

Solving for variable 'w'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + w = -14.908051516 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + w = -14.908051516 + 1.5
w = -14.908051516 + 1.5

Combine like terms: -14.908051516 + 1.5 = -13.408051516
w = -13.408051516

Simplifying
w = -13.408051516


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {16.408051516, -13.408051516}

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