y^2-14y+47=0

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Solution for y^2-14y+47=0 equation: 


Simplifying
y2 + -14y + 47 = 0

Reorder the terms:
47 + -14y + y2 = 0

Solving
47 + -14y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-47' to each side of the equation.
47 + -14y + -47 + y2 = 0 + -47

Reorder the terms:
47 + -47 + -14y + y2 = 0 + -47

Combine like terms: 47 + -47 = 0
0 + -14y + y2 = 0 + -47
-14y + y2 = 0 + -47

Combine like terms: 0 + -47 = -47
-14y + y2 = -47

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 = -47 + 49

Reorder the terms:
49 + -14y + y2 = -47 + 49

Combine like terms: -47 + 49 = 2
49 + -14y + y2 = 2

Factor a perfect square on the left side:
(y + -7)(y + -7) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(y + -7) equal to 1.414213562 and -1.414213562.


Subproblem 1
y + -7 = 1.414213562

Simplifying
y + -7 = 1.414213562

Reorder the terms:
-7 + y = 1.414213562

Solving
-7 + y = 1.414213562

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 = 1.414213562 + 7

Combine like terms: -7 + 7 = 0
0 + y = 1.414213562 + 7
y = 1.414213562 + 7

Combine like terms: 1.414213562 + 7 = 8.414213562
y = 8.414213562

Simplifying
y = 8.414213562


Subproblem 2
y + -7 = -1.414213562

Simplifying
y + -7 = -1.414213562

Reorder the terms:
-7 + y = -1.414213562

Solving
-7 + y = -1.414213562

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 = -1.414213562 + 7

Combine like terms: -7 + 7 = 0
0 + y = -1.414213562 + 7
y = -1.414213562 + 7

Combine like terms: -1.414213562 + 7 = 5.585786438
y = 5.585786438

Simplifying
y = 5.585786438


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {8.414213562, 5.585786438}

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