y^2-14y+38=0

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Solution for y^2-14y+38=0 equation:


Simplifying
y2 + -14y + 38 = 0

Reorder the terms:
38 + -14y + y2 = 0

Solving
38 + -14y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-38' to each side of the equation.
38 + -14y + -38 + y2 = 0 + -38

Reorder the terms:
38 + -38 + -14y + y2 = 0 + -38

Combine like terms: 38 + -38 = 0
0 + -14y + y2 = 0 + -38
-14y + y2 = 0 + -38

Combine like terms: 0 + -38 = -38
-14y + y2 = -38

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 = -38 + 49

Reorder the terms:
49 + -14y + y2 = -38 + 49

Combine like terms: -38 + 49 = 11
49 + -14y + y2 = 11

Factor a perfect square on the left side:
(y + -7)(y + -7) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(y + -7) equal to 3.31662479 and -3.31662479.


Subproblem 1
y + -7 = 3.31662479

Simplifying
y + -7 = 3.31662479

Reorder the terms:
-7 + y = 3.31662479

Solving
-7 + y = 3.31662479

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 = 3.31662479 + 7

Combine like terms: -7 + 7 = 0
0 + y = 3.31662479 + 7
y = 3.31662479 + 7

Combine like terms: 3.31662479 + 7 = 10.31662479
y = 10.31662479

Simplifying
y = 10.31662479


Subproblem 2
y + -7 = -3.31662479

Simplifying
y + -7 = -3.31662479

Reorder the terms:
-7 + y = -3.31662479

Solving
-7 + y = -3.31662479

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 = -3.31662479 + 7

Combine like terms: -7 + 7 = 0
0 + y = -3.31662479 + 7
y = -3.31662479 + 7

Combine like terms: -3.31662479 + 7 = 3.68337521
y = 3.68337521

Simplifying
y = 3.68337521


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {10.31662479, 3.68337521}

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