y^2-14y=-36

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


Simplifying
y2 + -14y = -36

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

Solving
-14y + y2 = -36

Solving for variable 'y'.

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

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

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 = 13
49 + -14y + y2 = 13

Factor a perfect square on the left side:
(y + -7)(y + -7) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(y + -7) equal to 3.605551275 and -3.605551275.


Subproblem 1
y + -7 = 3.605551275

Simplifying
y + -7 = 3.605551275

Reorder the terms:
-7 + y = 3.605551275

Solving
-7 + y = 3.605551275

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 = 3.605551275 + 7

Combine like terms: -7 + 7 = 0
0 + y = 3.605551275 + 7
y = 3.605551275 + 7

Combine like terms: 3.605551275 + 7 = 10.605551275
y = 10.605551275

Simplifying
y = 10.605551275


Subproblem 2
y + -7 = -3.605551275

Simplifying
y + -7 = -3.605551275

Reorder the terms:
-7 + y = -3.605551275

Solving
-7 + y = -3.605551275

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 = -3.605551275 + 7

Combine like terms: -7 + 7 = 0
0 + y = -3.605551275 + 7
y = -3.605551275 + 7

Combine like terms: -3.605551275 + 7 = 3.394448725
y = 3.394448725

Simplifying
y = 3.394448725


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {10.605551275, 3.394448725}

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