2y+y^2=14

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Solution for 2y+y^2=14 equation:


Simplifying
2y + y2 = 14

Solving
2y + y2 = 14

Solving for variable 'y'.

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

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

Begin completing the square.

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 = 2.872983346 y = 2.872983346 Simplifying y = 2.872983346

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 = -4.872983346 y = -4.872983346 Simplifying y = -4.872983346

Solution

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

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