y^2-4y-28=0

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Solution for y^2-4y-28=0 equation: 


Simplifying
y2 + -4y + -28 = 0

Reorder the terms:
-28 + -4y + y2 = 0

Solving
-28 + -4y + 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 + -4y + 28 + y2 = 0 + 28

Reorder the terms:
-28 + 28 + -4y + y2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -4y + y2 = 0 + 28
-4y + y2 = 0 + 28

Combine like terms: 0 + 28 = 28
-4y + y2 = 28

The y term is -4y.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4y + 4 + y2 = 28 + 4

Reorder the terms:
4 + -4y + y2 = 28 + 4

Combine like terms: 28 + 4 = 32
4 + -4y + y2 = 32

Factor a perfect square on the left side:
(y + -2)(y + -2) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(y + -2) equal to 5.656854249 and -5.656854249.


Subproblem 1
y + -2 = 5.656854249

Simplifying
y + -2 = 5.656854249

Reorder the terms:
-2 + y = 5.656854249

Solving
-2 + y = 5.656854249

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = 5.656854249 + 2

Combine like terms: -2 + 2 = 0
0 + y = 5.656854249 + 2
y = 5.656854249 + 2

Combine like terms: 5.656854249 + 2 = 7.656854249
y = 7.656854249

Simplifying
y = 7.656854249


Subproblem 2
y + -2 = -5.656854249

Simplifying
y + -2 = -5.656854249

Reorder the terms:
-2 + y = -5.656854249

Solving
-2 + y = -5.656854249

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = -5.656854249 + 2

Combine like terms: -2 + 2 = 0
0 + y = -5.656854249 + 2
y = -5.656854249 + 2

Combine like terms: -5.656854249 + 2 = -3.656854249
y = -3.656854249

Simplifying
y = -3.656854249


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {7.656854249, -3.656854249}

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