y^2-14y+28=0

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Solution for y^2-14y+28=0 equation: 


Simplifying
y2 + -14y + 28 = 0

Reorder the terms:
28 + -14y + y2 = 0

Solving
28 + -14y + 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 + -14y + -28 + y2 = 0 + -28

Reorder the terms:
28 + -28 + -14y + y2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -14y + y2 = 0 + -28
-14y + y2 = 0 + -28

Combine like terms: 0 + -28 = -28
-14y + y2 = -28

The y term is -14y.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14y + 49 + y2 = -28 + 49

Reorder the terms:
49 + -14y + y2 = -28 + 49

Combine like terms: -28 + 49 = 21
49 + -14y + y2 = 21

Factor a perfect square on the left side:
(y + -7)(y + -7) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(y + -7) equal to 4.582575695 and -4.582575695.


Subproblem 1
y + -7 = 4.582575695

Simplifying
y + -7 = 4.582575695

Reorder the terms:
-7 + y = 4.582575695

Solving
-7 + y = 4.582575695

Solving for variable 'y'.

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

Add '7' to each side of the equation.
-7 + 7 + y = 4.582575695 + 7

Combine like terms: -7 + 7 = 0
0 + y = 4.582575695 + 7
y = 4.582575695 + 7

Combine like terms: 4.582575695 + 7 = 11.582575695
y = 11.582575695

Simplifying
y = 11.582575695


Subproblem 2
y + -7 = -4.582575695

Simplifying
y + -7 = -4.582575695

Reorder the terms:
-7 + y = -4.582575695

Solving
-7 + y = -4.582575695

Solving for variable 'y'.

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

Add '7' to each side of the equation.
-7 + 7 + y = -4.582575695 + 7

Combine like terms: -7 + 7 = 0
0 + y = -4.582575695 + 7
y = -4.582575695 + 7

Combine like terms: -4.582575695 + 7 = 2.417424305
y = 2.417424305

Simplifying
y = 2.417424305


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {11.582575695, 2.417424305}

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