w^2+11w-28=0

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Solution for w^2+11w-28=0 equation: 


Simplifying
w2 + 11w + -28 = 0

Reorder the terms:
-28 + 11w + w2 = 0

Solving
-28 + 11w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 11w + 28 + w2 = 0 + 28

Reorder the terms:
-28 + 28 + 11w + w2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 11w + w2 = 0 + 28
11w + w2 = 0 + 28

Combine like terms: 0 + 28 = 28
11w + w2 = 28

The w term is 11w.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11w + 30.25 + w2 = 28 + 30.25

Reorder the terms:
30.25 + 11w + w2 = 28 + 30.25

Combine like terms: 28 + 30.25 = 58.25
30.25 + 11w + w2 = 58.25

Factor a perfect square on the left side:
(w + 5.5)(w + 5.5) = 58.25

Calculate the square root of the right side: 7.632168761

Break this problem into two subproblems by setting 
(w + 5.5) equal to 7.632168761 and -7.632168761.


Subproblem 1
w + 5.5 = 7.632168761

Simplifying
w + 5.5 = 7.632168761

Reorder the terms:
5.5 + w = 7.632168761

Solving
5.5 + w = 7.632168761

Solving for variable 'w'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + w = 7.632168761 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + w = 7.632168761 + -5.5
w = 7.632168761 + -5.5

Combine like terms: 7.632168761 + -5.5 = 2.132168761
w = 2.132168761

Simplifying
w = 2.132168761


Subproblem 2
w + 5.5 = -7.632168761

Simplifying
w + 5.5 = -7.632168761

Reorder the terms:
5.5 + w = -7.632168761

Solving
5.5 + w = -7.632168761

Solving for variable 'w'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + w = -7.632168761 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + w = -7.632168761 + -5.5
w = -7.632168761 + -5.5

Combine like terms: -7.632168761 + -5.5 = -13.132168761
w = -13.132168761

Simplifying
w = -13.132168761


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {2.132168761, -13.132168761}

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