w(w+.11)=.057

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Solution for w(w+.11)=.057 equation:


Simplifying
w(w + 0.11) = 0.057

Reorder the terms:
w(0.11 + w) = 0.057
(0.11 * w + w * w) = 0.057
(0.11w + w2) = 0.057

Solving
0.11w + w2 = 0.057

Solving for variable 'w'.

Reorder the terms:
-0.057 + 0.11w + w2 = 0.057 + -0.057

Combine like terms: 0.057 + -0.057 = 0.000
-0.057 + 0.11w + w2 = 0.000

Begin completing the square.

Move the constant term to the right:

Add '0.057' to each side of the equation.
-0.057 + 0.11w + 0.057 + w2 = 0.000 + 0.057

Reorder the terms:
-0.057 + 0.057 + 0.11w + w2 = 0.000 + 0.057

Combine like terms: -0.057 + 0.057 = 0.000
0.000 + 0.11w + w2 = 0.000 + 0.057
0.11w + w2 = 0.000 + 0.057

Combine like terms: 0.000 + 0.057 = 0.057
0.11w + w2 = 0.057

The w term is 0.11w.  Take half its coefficient (0.055).
Square it (0.003025) and add it to both sides.

Add '0.003025' to each side of the equation.
0.11w + 0.003025 + w2 = 0.057 + 0.003025

Reorder the terms:
0.003025 + 0.11w + w2 = 0.057 + 0.003025

Combine like terms: 0.057 + 0.003025 = 0.060025
0.003025 + 0.11w + w2 = 0.060025

Factor a perfect square on the left side:
(w + 0.055)(w + 0.055) = 0.060025

Calculate the square root of the right side: 0.245

Break this problem into two subproblems by setting 
(w + 0.055) equal to 0.245 and -0.245.

Subproblem 1

w + 0.055 = 0.245 Simplifying w + 0.055 = 0.245 Reorder the terms: 0.055 + w = 0.245 Solving 0.055 + w = 0.245 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.055' to each side of the equation. 0.055 + -0.055 + w = 0.245 + -0.055 Combine like terms: 0.055 + -0.055 = 0.000 0.000 + w = 0.245 + -0.055 w = 0.245 + -0.055 Combine like terms: 0.245 + -0.055 = 0.19 w = 0.19 Simplifying w = 0.19

Subproblem 2

w + 0.055 = -0.245 Simplifying w + 0.055 = -0.245 Reorder the terms: 0.055 + w = -0.245 Solving 0.055 + w = -0.245 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.055' to each side of the equation. 0.055 + -0.055 + w = -0.245 + -0.055 Combine like terms: 0.055 + -0.055 = 0.000 0.000 + w = -0.245 + -0.055 w = -0.245 + -0.055 Combine like terms: -0.245 + -0.055 = -0.3 w = -0.3 Simplifying w = -0.3

Solution

The solution to the problem is based on the solutions from the subproblems. w = {0.19, -0.3}

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