2y^2-4y=41

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Solution for 2y^2-4y=41 equation:


Simplifying
2y2 + -4y = 41

Reorder the terms:
-4y + 2y2 = 41

Solving
-4y + 2y2 = 41

Solving for variable 'y'.

Reorder the terms:
-41 + -4y + 2y2 = 41 + -41

Combine like terms: 41 + -41 = 0
-41 + -4y + 2y2 = 0

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

Divide each side by '2'.
-20.5 + -2y + y2 = 0

Move the constant term to the right:

Add '20.5' to each side of the equation.
-20.5 + -2y + 20.5 + y2 = 0 + 20.5

Reorder the terms:
-20.5 + 20.5 + -2y + y2 = 0 + 20.5

Combine like terms: -20.5 + 20.5 = 0.0
0.0 + -2y + y2 = 0 + 20.5
-2y + y2 = 0 + 20.5

Combine like terms: 0 + 20.5 = 20.5
-2y + y2 = 20.5

The y term is -2y.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2y + 1 + y2 = 20.5 + 1

Reorder the terms:
1 + -2y + y2 = 20.5 + 1

Combine like terms: 20.5 + 1 = 21.5
1 + -2y + y2 = 21.5

Factor a perfect square on the left side:
(y + -1)(y + -1) = 21.5

Calculate the square root of the right side: 4.636809248

Break this problem into two subproblems by setting 
(y + -1) equal to 4.636809248 and -4.636809248.

Subproblem 1

y + -1 = 4.636809248 Simplifying y + -1 = 4.636809248 Reorder the terms: -1 + y = 4.636809248 Solving -1 + y = 4.636809248 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 4.636809248 + 1 Combine like terms: -1 + 1 = 0 0 + y = 4.636809248 + 1 y = 4.636809248 + 1 Combine like terms: 4.636809248 + 1 = 5.636809248 y = 5.636809248 Simplifying y = 5.636809248

Subproblem 2

y + -1 = -4.636809248 Simplifying y + -1 = -4.636809248 Reorder the terms: -1 + y = -4.636809248 Solving -1 + y = -4.636809248 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -4.636809248 + 1 Combine like terms: -1 + 1 = 0 0 + y = -4.636809248 + 1 y = -4.636809248 + 1 Combine like terms: -4.636809248 + 1 = -3.636809248 y = -3.636809248 Simplifying y = -3.636809248

Solution

The solution to the problem is based on the solutions from the subproblems. y = {5.636809248, -3.636809248}

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