2y^2-y-(.5)=

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


Simplifying
2y2 + -1y + -1(0.5) = 0

Multiply -1 * 0.5
2y2 + -1y + -0.5 = 0

Reorder the terms:
-0.5 + -1y + 2y2 = 0

Solving
-0.5 + -1y + 2y2 = 0

Solving for variable 'y'.

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

Divide each side by '2'.
-0.25 + -0.5y + y2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -0.5y + 0.25 + y2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -0.5y + y2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -0.5y + y2 = 0 + 0.25
-0.5y + y2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-0.5y + y2 = 0.25

The y term is -0.5y.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5y + 0.0625 + y2 = 0.25 + 0.0625

Reorder the terms:
0.0625 + -0.5y + y2 = 0.25 + 0.0625

Combine like terms: 0.25 + 0.0625 = 0.3125
0.0625 + -0.5y + y2 = 0.3125

Factor a perfect square on the left side:
(y + -0.25)(y + -0.25) = 0.3125

Calculate the square root of the right side: 0.559016994

Break this problem into two subproblems by setting 
(y + -0.25) equal to 0.559016994 and -0.559016994.


Subproblem 1
y + -0.25 = 0.559016994

Simplifying
y + -0.25 = 0.559016994

Reorder the terms:
-0.25 + y = 0.559016994

Solving
-0.25 + y = 0.559016994

Solving for variable 'y'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + y = 0.559016994 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + y = 0.559016994 + 0.25
y = 0.559016994 + 0.25

Combine like terms: 0.559016994 + 0.25 = 0.809016994
y = 0.809016994

Simplifying
y = 0.809016994


Subproblem 2
y + -0.25 = -0.559016994

Simplifying
y + -0.25 = -0.559016994

Reorder the terms:
-0.25 + y = -0.559016994

Solving
-0.25 + y = -0.559016994

Solving for variable 'y'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + y = -0.559016994 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + y = -0.559016994 + 0.25
y = -0.559016994 + 0.25

Combine like terms: -0.559016994 + 0.25 = -0.309016994
y = -0.309016994

Simplifying
y = -0.309016994


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.809016994, -0.309016994}

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