2y^2-5y-8=0

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Solution for 2y^2-5y-8=0 equation:


Simplifying
2y2 + -5y + -8 = 0

Reorder the terms:
-8 + -5y + 2y2 = 0

Solving
-8 + -5y + 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'.
-4 + -2.5y + y2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -2.5y + 4 + y2 = 0 + 4

Reorder the terms:
-4 + 4 + -2.5y + y2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -2.5y + y2 = 0 + 4
-2.5y + y2 = 0 + 4

Combine like terms: 0 + 4 = 4
-2.5y + y2 = 4

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 = 4 + 1.5625

Reorder the terms:
1.5625 + -2.5y + y2 = 4 + 1.5625

Combine like terms: 4 + 1.5625 = 5.5625
1.5625 + -2.5y + y2 = 5.5625

Factor a perfect square on the left side:
(y + -1.25)(y + -1.25) = 5.5625

Calculate the square root of the right side: 2.358495283

Break this problem into two subproblems by setting 
(y + -1.25) equal to 2.358495283 and -2.358495283.

Subproblem 1

y + -1.25 = 2.358495283 Simplifying y + -1.25 = 2.358495283 Reorder the terms: -1.25 + y = 2.358495283 Solving -1.25 + y = 2.358495283 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 = 2.358495283 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + y = 2.358495283 + 1.25 y = 2.358495283 + 1.25 Combine like terms: 2.358495283 + 1.25 = 3.608495283 y = 3.608495283 Simplifying y = 3.608495283

Subproblem 2

y + -1.25 = -2.358495283 Simplifying y + -1.25 = -2.358495283 Reorder the terms: -1.25 + y = -2.358495283 Solving -1.25 + y = -2.358495283 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 = -2.358495283 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + y = -2.358495283 + 1.25 y = -2.358495283 + 1.25 Combine like terms: -2.358495283 + 1.25 = -1.108495283 y = -1.108495283 Simplifying y = -1.108495283

Solution

The solution to the problem is based on the solutions from the subproblems. y = {3.608495283, -1.108495283}

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