y^2-23y-28=0

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Solution for y^2-23y-28=0 equation: 


Simplifying
y2 + -23y + -28 = 0

Reorder the terms:
-28 + -23y + y2 = 0

Solving
-28 + -23y + 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 + -23y + 28 + y2 = 0 + 28

Reorder the terms:
-28 + 28 + -23y + y2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -23y + y2 = 0 + 28
-23y + y2 = 0 + 28

Combine like terms: 0 + 28 = 28
-23y + y2 = 28

The y term is -23y.  Take half its coefficient (-11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
-23y + 132.25 + y2 = 28 + 132.25

Reorder the terms:
132.25 + -23y + y2 = 28 + 132.25

Combine like terms: 28 + 132.25 = 160.25
132.25 + -23y + y2 = 160.25

Factor a perfect square on the left side:
(y + -11.5)(y + -11.5) = 160.25

Calculate the square root of the right side: 12.658988901

Break this problem into two subproblems by setting 
(y + -11.5) equal to 12.658988901 and -12.658988901.


Subproblem 1
y + -11.5 = 12.658988901

Simplifying
y + -11.5 = 12.658988901

Reorder the terms:
-11.5 + y = 12.658988901

Solving
-11.5 + y = 12.658988901

Solving for variable 'y'.

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

Add '11.5' to each side of the equation.
-11.5 + 11.5 + y = 12.658988901 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + y = 12.658988901 + 11.5
y = 12.658988901 + 11.5

Combine like terms: 12.658988901 + 11.5 = 24.158988901
y = 24.158988901

Simplifying
y = 24.158988901


Subproblem 2
y + -11.5 = -12.658988901

Simplifying
y + -11.5 = -12.658988901

Reorder the terms:
-11.5 + y = -12.658988901

Solving
-11.5 + y = -12.658988901

Solving for variable 'y'.

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

Add '11.5' to each side of the equation.
-11.5 + 11.5 + y = -12.658988901 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + y = -12.658988901 + 11.5
y = -12.658988901 + 11.5

Combine like terms: -12.658988901 + 11.5 = -1.158988901
y = -1.158988901

Simplifying
y = -1.158988901


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {24.158988901, -1.158988901}

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