1.66=2.23w-w^2+3.98

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Solution for 1.66=2.23w-w^2+3.98 equation: 


Simplifying
1.66 = 2.23w + -1w2 + 3.98

Reorder the terms:
1.66 = 3.98 + 2.23w + -1w2

Solving
1.66 = 3.98 + 2.23w + -1w2

Solving for variable 'w'.

Combine like terms: 1.66 + -3.98 = -2.32
-2.32 + -2.23w + w2 = 3.98 + 2.23w + -1w2 + -3.98 + -2.23w + w2

Reorder the terms:
-2.32 + -2.23w + w2 = 3.98 + -3.98 + 2.23w + -2.23w + -1w2 + w2

Combine like terms: 3.98 + -3.98 = 0.00
-2.32 + -2.23w + w2 = 0.00 + 2.23w + -2.23w + -1w2 + w2
-2.32 + -2.23w + w2 = 2.23w + -2.23w + -1w2 + w2

Combine like terms: 2.23w + -2.23w = 0.00
-2.32 + -2.23w + w2 = 0.00 + -1w2 + w2
-2.32 + -2.23w + w2 = -1w2 + w2

Combine like terms: -1w2 + w2 = 0
-2.32 + -2.23w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2.32' to each side of the equation.
-2.32 + -2.23w + 2.32 + w2 = 0 + 2.32

Reorder the terms:
-2.32 + 2.32 + -2.23w + w2 = 0 + 2.32

Combine like terms: -2.32 + 2.32 = 0.00
0.00 + -2.23w + w2 = 0 + 2.32
-2.23w + w2 = 0 + 2.32

Combine like terms: 0 + 2.32 = 2.32
-2.23w + w2 = 2.32

The w term is -2.23w.  Take half its coefficient (-1.115).
Square it (1.243225) and add it to both sides.

Add '1.243225' to each side of the equation.
-2.23w + 1.243225 + w2 = 2.32 + 1.243225

Reorder the terms:
1.243225 + -2.23w + w2 = 2.32 + 1.243225

Combine like terms: 2.32 + 1.243225 = 3.563225
1.243225 + -2.23w + w2 = 3.563225

Factor a perfect square on the left side:
(w + -1.115)(w + -1.115) = 3.563225

Calculate the square root of the right side: 1.887650656

Break this problem into two subproblems by setting 
(w + -1.115) equal to 1.887650656 and -1.887650656.


Subproblem 1
w + -1.115 = 1.887650656

Simplifying
w + -1.115 = 1.887650656

Reorder the terms:
-1.115 + w = 1.887650656

Solving
-1.115 + w = 1.887650656

Solving for variable 'w'.

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

Add '1.115' to each side of the equation.
-1.115 + 1.115 + w = 1.887650656 + 1.115

Combine like terms: -1.115 + 1.115 = 0.000
0.000 + w = 1.887650656 + 1.115
w = 1.887650656 + 1.115

Combine like terms: 1.887650656 + 1.115 = 3.002650656
w = 3.002650656

Simplifying
w = 3.002650656


Subproblem 2
w + -1.115 = -1.887650656

Simplifying
w + -1.115 = -1.887650656

Reorder the terms:
-1.115 + w = -1.887650656

Solving
-1.115 + w = -1.887650656

Solving for variable 'w'.

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

Add '1.115' to each side of the equation.
-1.115 + 1.115 + w = -1.887650656 + 1.115

Combine like terms: -1.115 + 1.115 = 0.000
0.000 + w = -1.887650656 + 1.115
w = -1.887650656 + 1.115

Combine like terms: -1.887650656 + 1.115 = -0.772650656
w = -0.772650656

Simplifying
w = -0.772650656


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {3.002650656, -0.772650656}

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