y^2-14y-36=0

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Solution for y^2-14y-36=0 equation: 


Simplifying
y2 + -14y + -36 = 0

Reorder the terms:
-36 + -14y + y2 = 0

Solving
-36 + -14y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -14y + 36 + y2 = 0 + 36

Reorder the terms:
-36 + 36 + -14y + y2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -14y + y2 = 0 + 36
-14y + y2 = 0 + 36

Combine like terms: 0 + 36 = 36
-14y + y2 = 36

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 = 36 + 49

Reorder the terms:
49 + -14y + y2 = 36 + 49

Combine like terms: 36 + 49 = 85
49 + -14y + y2 = 85

Factor a perfect square on the left side:
(y + -7)(y + -7) = 85

Calculate the square root of the right side: 9.219544457

Break this problem into two subproblems by setting 
(y + -7) equal to 9.219544457 and -9.219544457.


Subproblem 1
y + -7 = 9.219544457

Simplifying
y + -7 = 9.219544457

Reorder the terms:
-7 + y = 9.219544457

Solving
-7 + y = 9.219544457

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 = 9.219544457 + 7

Combine like terms: -7 + 7 = 0
0 + y = 9.219544457 + 7
y = 9.219544457 + 7

Combine like terms: 9.219544457 + 7 = 16.219544457
y = 16.219544457

Simplifying
y = 16.219544457


Subproblem 2
y + -7 = -9.219544457

Simplifying
y + -7 = -9.219544457

Reorder the terms:
-7 + y = -9.219544457

Solving
-7 + y = -9.219544457

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 = -9.219544457 + 7

Combine like terms: -7 + 7 = 0
0 + y = -9.219544457 + 7
y = -9.219544457 + 7

Combine like terms: -9.219544457 + 7 = -2.219544457
y = -2.219544457

Simplifying
y = -2.219544457


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {16.219544457, -2.219544457}

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