5(-6.6+0.2y)y=23

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Solution for 5(-6.6+0.2y)y=23 equation: 


Simplifying
5(-6.6 + 0.2y) * y = 23

Reorder the terms for easier multiplication:
5y(-6.6 + 0.2y) = 23
(-6.6 * 5y + 0.2y * 5y) = 23
(-33y + 1y2) = 23

Solving
-33y + 1y2 = 23

Solving for variable 'y'.

Reorder the terms:
-23 + -33y + 1y2 = 23 + -23

Combine like terms: 23 + -23 = 0
-23 + -33y + 1y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + -33y + 23 + y2 = 0 + 23

Reorder the terms:
-23 + 23 + -33y + y2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -33y + y2 = 0 + 23
-33y + y2 = 0 + 23

Combine like terms: 0 + 23 = 23
-33y + y2 = 23

The y term is -33y.  Take half its coefficient (-16.5).
Square it (272.25) and add it to both sides.

Add '272.25' to each side of the equation.
-33y + 272.25 + y2 = 23 + 272.25

Reorder the terms:
272.25 + -33y + y2 = 23 + 272.25

Combine like terms: 23 + 272.25 = 295.25
272.25 + -33y + y2 = 295.25

Factor a perfect square on the left side:
(y + -16.5)(y + -16.5) = 295.25

Calculate the square root of the right side: 17.182840277

Break this problem into two subproblems by setting 
(y + -16.5) equal to 17.182840277 and -17.182840277.


Subproblem 1
y + -16.5 = 17.182840277

Simplifying
y + -16.5 = 17.182840277

Reorder the terms:
-16.5 + y = 17.182840277

Solving
-16.5 + y = 17.182840277

Solving for variable 'y'.

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

Add '16.5' to each side of the equation.
-16.5 + 16.5 + y = 17.182840277 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + y = 17.182840277 + 16.5
y = 17.182840277 + 16.5

Combine like terms: 17.182840277 + 16.5 = 33.682840277
y = 33.682840277

Simplifying
y = 33.682840277


Subproblem 2
y + -16.5 = -17.182840277

Simplifying
y + -16.5 = -17.182840277

Reorder the terms:
-16.5 + y = -17.182840277

Solving
-16.5 + y = -17.182840277

Solving for variable 'y'.

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

Add '16.5' to each side of the equation.
-16.5 + 16.5 + y = -17.182840277 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + y = -17.182840277 + 16.5
y = -17.182840277 + 16.5

Combine like terms: -17.182840277 + 16.5 = -0.682840277
y = -0.682840277

Simplifying
y = -0.682840277


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {33.682840277, -0.682840277}

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