2(2y^2+2y-5)=8.144

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Solution for 2(2y^2+2y-5)=8.144 equation: 


Simplifying
2(2y2 + 2y + -5) = 8.144

Reorder the terms:
2(-5 + 2y + 2y2) = 8.144
(-5 * 2 + 2y * 2 + 2y2 * 2) = 8.144
(-10 + 4y + 4y2) = 8.144

Solving
-10 + 4y + 4y2 = 8.144

Solving for variable 'y'.

Reorder the terms:
-10 + -8.144 + 4y + 4y2 = 8.144 + -8.144

Combine like terms: -10 + -8.144 = -18.144
-18.144 + 4y + 4y2 = 8.144 + -8.144

Combine like terms: 8.144 + -8.144 = 0.000
-18.144 + 4y + 4y2 = 0.000

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

Divide each side by '4'.
-4.536 + y + y2 = 0.000

Move the constant term to the right:

Add '4.536' to each side of the equation.
-4.536 + y + 4.536 + y2 = 0.000 + 4.536

Reorder the terms:
-4.536 + 4.536 + y + y2 = 0.000 + 4.536

Combine like terms: -4.536 + 4.536 = 0.000
0.000 + y + y2 = 0.000 + 4.536
y + y2 = 0.000 + 4.536

Combine like terms: 0.000 + 4.536 = 4.536
y + y2 = 4.536

The y term is y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + y2 = 4.536 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + y2 = 4.536 + 0.25

Combine like terms: 4.536 + 0.25 = 4.786
1.25 + y2 = 4.786

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 4.786

Calculate the square root of the right side: 2.187692849

Break this problem into two subproblems by setting 
(y + 0.5) equal to 2.187692849 and -2.187692849.


Subproblem 1
y + 0.5 = 2.187692849

Simplifying
y + 0.5 = 2.187692849

Reorder the terms:
0.5 + y = 2.187692849

Solving
0.5 + y = 2.187692849

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = 2.187692849 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 2.187692849 + -0.5
y = 2.187692849 + -0.5

Combine like terms: 2.187692849 + -0.5 = 1.687692849
y = 1.687692849

Simplifying
y = 1.687692849


Subproblem 2
y + 0.5 = -2.187692849

Simplifying
y + 0.5 = -2.187692849

Reorder the terms:
0.5 + y = -2.187692849

Solving
0.5 + y = -2.187692849

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = -2.187692849 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -2.187692849 + -0.5
y = -2.187692849 + -0.5

Combine like terms: -2.187692849 + -0.5 = -2.687692849
y = -2.687692849

Simplifying
y = -2.687692849


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.687692849, -2.687692849}

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