y^2+11y-28=0

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


Simplifying
y2 + 11y + -28 = 0

Reorder the terms:
-28 + 11y + y2 = 0

Solving
-28 + 11y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 11y + 28 + y2 = 0 + 28

Reorder the terms:
-28 + 28 + 11y + y2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 11y + y2 = 0 + 28
11y + y2 = 0 + 28

Combine like terms: 0 + 28 = 28
11y + y2 = 28

The y term is 11y.  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.
11y + 30.25 + y2 = 28 + 30.25

Reorder the terms:
30.25 + 11y + y2 = 28 + 30.25

Combine like terms: 28 + 30.25 = 58.25
30.25 + 11y + y2 = 58.25

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

Calculate the square root of the right side: 7.632168761

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


Subproblem 1
y + 5.5 = 7.632168761

Simplifying
y + 5.5 = 7.632168761

Reorder the terms:
5.5 + y = 7.632168761

Solving
5.5 + y = 7.632168761

Solving for variable 'y'.

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

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

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

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

Simplifying
y = 2.132168761


Subproblem 2
y + 5.5 = -7.632168761

Simplifying
y + 5.5 = -7.632168761

Reorder the terms:
5.5 + y = -7.632168761

Solving
5.5 + y = -7.632168761

Solving for variable 'y'.

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

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

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

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

Simplifying
y = -13.132168761


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

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