y^2+4y=2

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


Simplifying
y2 + 4y = 2

Reorder the terms:
4y + y2 = 2

Solving
4y + y2 = 2

Solving for variable 'y'.

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The y term is 4y.  Take half its coefficient (2).
Square it (4) and add it to both sides.

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

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

Combine like terms: 2 + 4 = 6
4 + 4y + y2 = 6

Factor a perfect square on the left side:
(y + 2)(y + 2) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(y + 2) equal to 2.449489743 and -2.449489743.


Subproblem 1
y + 2 = 2.449489743

Simplifying
y + 2 = 2.449489743

Reorder the terms:
2 + y = 2.449489743

Solving
2 + y = 2.449489743

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + y = 2.449489743 + -2

Combine like terms: 2 + -2 = 0
0 + y = 2.449489743 + -2
y = 2.449489743 + -2

Combine like terms: 2.449489743 + -2 = 0.449489743
y = 0.449489743

Simplifying
y = 0.449489743


Subproblem 2
y + 2 = -2.449489743

Simplifying
y + 2 = -2.449489743

Reorder the terms:
2 + y = -2.449489743

Solving
2 + y = -2.449489743

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + y = -2.449489743 + -2

Combine like terms: 2 + -2 = 0
0 + y = -2.449489743 + -2
y = -2.449489743 + -2

Combine like terms: -2.449489743 + -2 = -4.449489743
y = -4.449489743

Simplifying
y = -4.449489743


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.449489743, -4.449489743}

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