y^2-14y-8=0

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


Simplifying
y2 + -14y + -8 = 0

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

Solving
-8 + -14y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 8 + 49

Reorder the terms:
49 + -14y + y2 = 8 + 49

Combine like terms: 8 + 49 = 57
49 + -14y + y2 = 57

Factor a perfect square on the left side:
(y + -7)(y + -7) = 57

Calculate the square root of the right side: 7.549834435

Break this problem into two subproblems by setting 
(y + -7) equal to 7.549834435 and -7.549834435.


Subproblem 1
y + -7 = 7.549834435

Simplifying
y + -7 = 7.549834435

Reorder the terms:
-7 + y = 7.549834435

Solving
-7 + y = 7.549834435

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 = 7.549834435 + 7

Combine like terms: -7 + 7 = 0
0 + y = 7.549834435 + 7
y = 7.549834435 + 7

Combine like terms: 7.549834435 + 7 = 14.549834435
y = 14.549834435

Simplifying
y = 14.549834435


Subproblem 2
y + -7 = -7.549834435

Simplifying
y + -7 = -7.549834435

Reorder the terms:
-7 + y = -7.549834435

Solving
-7 + y = -7.549834435

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 = -7.549834435 + 7

Combine like terms: -7 + 7 = 0
0 + y = -7.549834435 + 7
y = -7.549834435 + 7

Combine like terms: -7.549834435 + 7 = -0.549834435
y = -0.549834435

Simplifying
y = -0.549834435


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {14.549834435, -0.549834435}

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