1-2y^2+y=9y+2

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Solution for 1-2y^2+y=9y+2 equation: 


Simplifying
1 + -2y2 + y = 9y + 2

Reorder the terms:
1 + y + -2y2 = 9y + 2

Reorder the terms:
1 + y + -2y2 = 2 + 9y

Solving
1 + y + -2y2 = 2 + 9y

Solving for variable 'y'.

Reorder the terms:
1 + -2 + y + -9y + -2y2 = 2 + 9y + -2 + -9y

Combine like terms: 1 + -2 = -1
-1 + y + -9y + -2y2 = 2 + 9y + -2 + -9y

Combine like terms: y + -9y = -8y
-1 + -8y + -2y2 = 2 + 9y + -2 + -9y

Reorder the terms:
-1 + -8y + -2y2 = 2 + -2 + 9y + -9y

Combine like terms: 2 + -2 = 0
-1 + -8y + -2y2 = 0 + 9y + -9y
-1 + -8y + -2y2 = 9y + -9y

Combine like terms: 9y + -9y = 0
-1 + -8y + -2y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 8y + 2y2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(1 + 8y + 2y2)' equal to zero and attempt to solve:

Simplifying
1 + 8y + 2y2 = 0

Solving
1 + 8y + 2y2 = 0

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

Divide each side by '2'.
0.5 + 4y + y2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 4y + -0.5 + y2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 4y + y2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 4y + y2 = 0 + -0.5
4y + y2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
4y + y2 = -0.5

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 = -0.5 + 4

Reorder the terms:
4 + 4y + y2 = -0.5 + 4

Combine like terms: -0.5 + 4 = 3.5
4 + 4y + y2 = 3.5

Factor a perfect square on the left side:
(y + 2)(y + 2) = 3.5

Calculate the square root of the right side: 1.870828693

Break this problem into two subproblems by setting 
(y + 2) equal to 1.870828693 and -1.870828693.


Subproblem 1
y + 2 = 1.870828693

Simplifying
y + 2 = 1.870828693

Reorder the terms:
2 + y = 1.870828693

Solving
2 + y = 1.870828693

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 = 1.870828693 + -2

Combine like terms: 2 + -2 = 0
0 + y = 1.870828693 + -2
y = 1.870828693 + -2

Combine like terms: 1.870828693 + -2 = -0.129171307
y = -0.129171307

Simplifying
y = -0.129171307


Subproblem 2
y + 2 = -1.870828693

Simplifying
y + 2 = -1.870828693

Reorder the terms:
2 + y = -1.870828693

Solving
2 + y = -1.870828693

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 = -1.870828693 + -2

Combine like terms: 2 + -2 = 0
0 + y = -1.870828693 + -2
y = -1.870828693 + -2

Combine like terms: -1.870828693 + -2 = -3.870828693
y = -3.870828693

Simplifying
y = -3.870828693


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.129171307, -3.870828693}
Solution
y = {-0.129171307, -3.870828693}

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