(y+7)+(y+7)=y^2

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Solution for (y+7)+(y+7)=y^2 equation:


Simplifying
(y + 7) + (y + 7) = y2

Reorder the terms:
(7 + y) + (y + 7) = y2

Remove parenthesis around (7 + y)
7 + y + (y + 7) = y2

Reorder the terms:
7 + y + (7 + y) = y2

Remove parenthesis around (7 + y)
7 + y + 7 + y = y2

Reorder the terms:
7 + 7 + y + y = y2

Combine like terms: 7 + 7 = 14
14 + y + y = y2

Combine like terms: y + y = 2y
14 + 2y = y2

Solving
14 + 2y = y2

Solving for variable 'y'.

Combine like terms: y2 + -1y2 = 0
14 + 2y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-14 + -2y + y2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -2y + 14 + y2 = 0 + 14

Reorder the terms:
-14 + 14 + -2y + y2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -2y + y2 = 0 + 14
-2y + y2 = 0 + 14

Combine like terms: 0 + 14 = 14
-2y + y2 = 14

The y term is -2y.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2y + 1 + y2 = 14 + 1

Reorder the terms:
1 + -2y + y2 = 14 + 1

Combine like terms: 14 + 1 = 15
1 + -2y + y2 = 15

Factor a perfect square on the left side:
(y + -1)(y + -1) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(y + -1) equal to 3.872983346 and -3.872983346.

Subproblem 1

y + -1 = 3.872983346 Simplifying y + -1 = 3.872983346 Reorder the terms: -1 + y = 3.872983346 Solving -1 + y = 3.872983346 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 3.872983346 + 1 Combine like terms: -1 + 1 = 0 0 + y = 3.872983346 + 1 y = 3.872983346 + 1 Combine like terms: 3.872983346 + 1 = 4.872983346 y = 4.872983346 Simplifying y = 4.872983346

Subproblem 2

y + -1 = -3.872983346 Simplifying y + -1 = -3.872983346 Reorder the terms: -1 + y = -3.872983346 Solving -1 + y = -3.872983346 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -3.872983346 + 1 Combine like terms: -1 + 1 = 0 0 + y = -3.872983346 + 1 y = -3.872983346 + 1 Combine like terms: -3.872983346 + 1 = -2.872983346 y = -2.872983346 Simplifying y = -2.872983346

Solution

The solution to the problem is based on the solutions from the subproblems. y = {4.872983346, -2.872983346}

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