(y^2)-8y+14=0

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Solution for (y^2)-8y+14=0 equation: 


Simplifying
(y2) + -8y + 14 = 0
y2 + -8y + 14 = 0

Reorder the terms:
14 + -8y + y2 = 0

Solving
14 + -8y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + -8y + -14 + y2 = 0 + -14

Reorder the terms:
14 + -14 + -8y + y2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -8y + y2 = 0 + -14
-8y + y2 = 0 + -14

Combine like terms: 0 + -14 = -14
-8y + y2 = -14

The y term is -8y.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8y + 16 + y2 = -14 + 16

Reorder the terms:
16 + -8y + y2 = -14 + 16

Combine like terms: -14 + 16 = 2
16 + -8y + y2 = 2

Factor a perfect square on the left side:
(y + -4)(y + -4) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(y + -4) equal to 1.414213562 and -1.414213562.


Subproblem 1
y + -4 = 1.414213562

Simplifying
y + -4 = 1.414213562

Reorder the terms:
-4 + y = 1.414213562

Solving
-4 + y = 1.414213562

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = 1.414213562 + 4

Combine like terms: -4 + 4 = 0
0 + y = 1.414213562 + 4
y = 1.414213562 + 4

Combine like terms: 1.414213562 + 4 = 5.414213562
y = 5.414213562

Simplifying
y = 5.414213562


Subproblem 2
y + -4 = -1.414213562

Simplifying
y + -4 = -1.414213562

Reorder the terms:
-4 + y = -1.414213562

Solving
-4 + y = -1.414213562

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = -1.414213562 + 4

Combine like terms: -4 + 4 = 0
0 + y = -1.414213562 + 4
y = -1.414213562 + 4

Combine like terms: -1.414213562 + 4 = 2.585786438
y = 2.585786438

Simplifying
y = 2.585786438


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.414213562, 2.585786438}

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