22=(2w+3.5)w

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Solution for 22=(2w+3.5)w equation: 


Simplifying
22 = (2w + 3.5) * w

Reorder the terms:
22 = (3.5 + 2w) * w

Reorder the terms for easier multiplication:
22 = w(3.5 + 2w)
22 = (3.5 * w + 2w * w)
22 = (3.5w + 2w2)

Solving
22 = 3.5w + 2w2

Solving for variable 'w'.

Reorder the terms:
22 + -3.5w + -2w2 = 3.5w + -3.5w + 2w2 + -2w2

Combine like terms: 3.5w + -3.5w = 0.0
22 + -3.5w + -2w2 = 0.0 + 2w2 + -2w2
22 + -3.5w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
22 + -3.5w + -2w2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-11 + 1.75w + w2 = 0

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 1.75w + 11 + w2 = 0 + 11

Reorder the terms:
-11 + 11 + 1.75w + w2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 1.75w + w2 = 0 + 11
1.75w + w2 = 0 + 11

Combine like terms: 0 + 11 = 11
1.75w + w2 = 11

The w term is 1.75w.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75w + 0.765625 + w2 = 11 + 0.765625

Reorder the terms:
0.765625 + 1.75w + w2 = 11 + 0.765625

Combine like terms: 11 + 0.765625 = 11.765625
0.765625 + 1.75w + w2 = 11.765625

Factor a perfect square on the left side:
(w + 0.875)(w + 0.875) = 11.765625

Calculate the square root of the right side: 3.430105684

Break this problem into two subproblems by setting 
(w + 0.875) equal to 3.430105684 and -3.430105684.


Subproblem 1
w + 0.875 = 3.430105684

Simplifying
w + 0.875 = 3.430105684

Reorder the terms:
0.875 + w = 3.430105684

Solving
0.875 + w = 3.430105684

Solving for variable 'w'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + w = 3.430105684 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + w = 3.430105684 + -0.875
w = 3.430105684 + -0.875

Combine like terms: 3.430105684 + -0.875 = 2.555105684
w = 2.555105684

Simplifying
w = 2.555105684


Subproblem 2
w + 0.875 = -3.430105684

Simplifying
w + 0.875 = -3.430105684

Reorder the terms:
0.875 + w = -3.430105684

Solving
0.875 + w = -3.430105684

Solving for variable 'w'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + w = -3.430105684 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + w = -3.430105684 + -0.875
w = -3.430105684 + -0.875

Combine like terms: -3.430105684 + -0.875 = -4.305105684
w = -4.305105684

Simplifying
w = -4.305105684


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {2.555105684, -4.305105684}

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