2y^2-5y=54

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Solution for 2y^2-5y=54 equation:


Simplifying
2y2 + -5y = 54

Reorder the terms:
-5y + 2y2 = 54

Solving
-5y + 2y2 = 54

Solving for variable 'y'.

Reorder the terms:
-54 + -5y + 2y2 = 54 + -54

Combine like terms: 54 + -54 = 0
-54 + -5y + 2y2 = 0

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

Divide each side by '2'.
-27 + -2.5y + y2 = 0

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + -2.5y + 27 + y2 = 0 + 27

Reorder the terms:
-27 + 27 + -2.5y + y2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -2.5y + y2 = 0 + 27
-2.5y + y2 = 0 + 27

Combine like terms: 0 + 27 = 27
-2.5y + y2 = 27

The y term is -2.5y.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5y + 1.5625 + y2 = 27 + 1.5625

Reorder the terms:
1.5625 + -2.5y + y2 = 27 + 1.5625

Combine like terms: 27 + 1.5625 = 28.5625
1.5625 + -2.5y + y2 = 28.5625

Factor a perfect square on the left side:
(y + -1.25)(y + -1.25) = 28.5625

Calculate the square root of the right side: 5.344389582

Break this problem into two subproblems by setting 
(y + -1.25) equal to 5.344389582 and -5.344389582.

Subproblem 1

y + -1.25 = 5.344389582 Simplifying y + -1.25 = 5.344389582 Reorder the terms: -1.25 + y = 5.344389582 Solving -1.25 + y = 5.344389582 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + y = 5.344389582 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + y = 5.344389582 + 1.25 y = 5.344389582 + 1.25 Combine like terms: 5.344389582 + 1.25 = 6.594389582 y = 6.594389582 Simplifying y = 6.594389582

Subproblem 2

y + -1.25 = -5.344389582 Simplifying y + -1.25 = -5.344389582 Reorder the terms: -1.25 + y = -5.344389582 Solving -1.25 + y = -5.344389582 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + y = -5.344389582 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + y = -5.344389582 + 1.25 y = -5.344389582 + 1.25 Combine like terms: -5.344389582 + 1.25 = -4.094389582 y = -4.094389582 Simplifying y = -4.094389582

Solution

The solution to the problem is based on the solutions from the subproblems. y = {6.594389582, -4.094389582}

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