2y^2+8y+6=4

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Solution for 2y^2+8y+6=4 equation: 


Simplifying
2y2 + 8y + 6 = 4

Reorder the terms:
6 + 8y + 2y2 = 4

Solving
6 + 8y + 2y2 = 4

Solving for variable 'y'.

Reorder the terms:
6 + -4 + 8y + 2y2 = 4 + -4

Combine like terms: 6 + -4 = 2
2 + 8y + 2y2 = 4 + -4

Combine like terms: 4 + -4 = 0
2 + 8y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 4y + y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + 4y + y2)' equal to zero and attempt to solve:

Simplifying
1 + 4y + y2 = 0

Solving
1 + 4y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 4y + -1 + y2 = 0 + -1

Reorder the terms:
1 + -1 + 4y + y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4y + y2 = 0 + -1
4y + y2 = 0 + -1

Combine like terms: 0 + -1 = -1
4y + y2 = -1

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 = -1 + 4

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

Combine like terms: -1 + 4 = 3
4 + 4y + y2 = 3

Factor a perfect square on the left side:
(y + 2)(y + 2) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(y + 2) equal to 1.732050808 and -1.732050808.


Subproblem 1
y + 2 = 1.732050808

Simplifying
y + 2 = 1.732050808

Reorder the terms:
2 + y = 1.732050808

Solving
2 + y = 1.732050808

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 = 1.732050808 + -2

Combine like terms: 2 + -2 = 0
0 + y = 1.732050808 + -2
y = 1.732050808 + -2

Combine like terms: 1.732050808 + -2 = -0.267949192
y = -0.267949192

Simplifying
y = -0.267949192


Subproblem 2
y + 2 = -1.732050808

Simplifying
y + 2 = -1.732050808

Reorder the terms:
2 + y = -1.732050808

Solving
2 + y = -1.732050808

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 = -1.732050808 + -2

Combine like terms: 2 + -2 = 0
0 + y = -1.732050808 + -2
y = -1.732050808 + -2

Combine like terms: -1.732050808 + -2 = -3.732050808
y = -3.732050808

Simplifying
y = -3.732050808


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.267949192, -3.732050808}
Solution
y = {-0.267949192, -3.732050808}

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