y^2=2y+4

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Solution for y^2=2y+4 equation:


Simplifying
y2 = 2y + 4

Reorder the terms:
y2 = 4 + 2y

Solving
y2 = 4 + 2y

Solving for variable 'y'.

Reorder the terms:
-4 + -2y + y2 = 4 + 2y + -4 + -2y

Reorder the terms:
-4 + -2y + y2 = 4 + -4 + 2y + -2y

Combine like terms: 4 + -4 = 0
-4 + -2y + y2 = 0 + 2y + -2y
-4 + -2y + y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
-4 + -2y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -2y + 4 + y2 = 0 + 4

Reorder the terms:
-4 + 4 + -2y + y2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -2y + y2 = 0 + 4
-2y + y2 = 0 + 4

Combine like terms: 0 + 4 = 4
-2y + y2 = 4

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 = 4 + 1

Reorder the terms:
1 + -2y + y2 = 4 + 1

Combine like terms: 4 + 1 = 5
1 + -2y + y2 = 5

Factor a perfect square on the left side:
(y + -1)(y + -1) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(y + -1) equal to 2.236067978 and -2.236067978.

Subproblem 1

y + -1 = 2.236067978 Simplifying y + -1 = 2.236067978 Reorder the terms: -1 + y = 2.236067978 Solving -1 + y = 2.236067978 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 = 2.236067978 + 1 Combine like terms: -1 + 1 = 0 0 + y = 2.236067978 + 1 y = 2.236067978 + 1 Combine like terms: 2.236067978 + 1 = 3.236067978 y = 3.236067978 Simplifying y = 3.236067978

Subproblem 2

y + -1 = -2.236067978 Simplifying y + -1 = -2.236067978 Reorder the terms: -1 + y = -2.236067978 Solving -1 + y = -2.236067978 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 = -2.236067978 + 1 Combine like terms: -1 + 1 = 0 0 + y = -2.236067978 + 1 y = -2.236067978 + 1 Combine like terms: -2.236067978 + 1 = -1.236067978 y = -1.236067978 Simplifying y = -1.236067978

Solution

The solution to the problem is based on the solutions from the subproblems. y = {3.236067978, -1.236067978}

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