2y^2-6y=16

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Solution for 2y^2-6y=16 equation: 


Simplifying
2y2 + -6y = 16

Reorder the terms:
-6y + 2y2 = 16

Solving
-6y + 2y2 = 16

Solving for variable 'y'.

Reorder the terms:
-16 + -6y + 2y2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + -6y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -3y + y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + -3y + y2)' equal to zero and attempt to solve:

Simplifying
-8 + -3y + y2 = 0

Solving
-8 + -3y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -3y + 8 + y2 = 0 + 8

Reorder the terms:
-8 + 8 + -3y + y2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3y + y2 = 0 + 8
-3y + y2 = 0 + 8

Combine like terms: 0 + 8 = 8
-3y + y2 = 8

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = 8 + 2.25

Reorder the terms:
2.25 + -3y + y2 = 8 + 2.25

Combine like terms: 8 + 2.25 = 10.25
2.25 + -3y + y2 = 10.25

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(y + -1.5) equal to 3.201562119 and -3.201562119.


Subproblem 1
y + -1.5 = 3.201562119

Simplifying
y + -1.5 = 3.201562119

Reorder the terms:
-1.5 + y = 3.201562119

Solving
-1.5 + y = 3.201562119

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = 3.201562119 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = 3.201562119 + 1.5
y = 3.201562119 + 1.5

Combine like terms: 3.201562119 + 1.5 = 4.701562119
y = 4.701562119

Simplifying
y = 4.701562119


Subproblem 2
y + -1.5 = -3.201562119

Simplifying
y + -1.5 = -3.201562119

Reorder the terms:
-1.5 + y = -3.201562119

Solving
-1.5 + y = -3.201562119

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = -3.201562119 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = -3.201562119 + 1.5
y = -3.201562119 + 1.5

Combine like terms: -3.201562119 + 1.5 = -1.701562119
y = -1.701562119

Simplifying
y = -1.701562119


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.701562119, -1.701562119}
Solution
y = {4.701562119, -1.701562119}

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