2y^2-11y+8=0

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Solution for 2y^2-11y+8=0 equation:


Simplifying
2y2 + -11y + 8 = 0

Reorder the terms:
8 + -11y + 2y2 = 0

Solving
8 + -11y + 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 + -5.5y + y2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -5.5y + -4 + y2 = 0 + -4

Reorder the terms:
4 + -4 + -5.5y + y2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5.5y + y2 = 0 + -4
-5.5y + y2 = 0 + -4

Combine like terms: 0 + -4 = -4
-5.5y + y2 = -4

The y term is -5.5y.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5y + 7.5625 + y2 = -4 + 7.5625

Reorder the terms:
7.5625 + -5.5y + y2 = -4 + 7.5625

Combine like terms: -4 + 7.5625 = 3.5625
7.5625 + -5.5y + y2 = 3.5625

Factor a perfect square on the left side:
(y + -2.75)(y + -2.75) = 3.5625

Calculate the square root of the right side: 1.887458609

Break this problem into two subproblems by setting 
(y + -2.75) equal to 1.887458609 and -1.887458609.

Subproblem 1

y + -2.75 = 1.887458609 Simplifying y + -2.75 = 1.887458609 Reorder the terms: -2.75 + y = 1.887458609 Solving -2.75 + y = 1.887458609 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + y = 1.887458609 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + y = 1.887458609 + 2.75 y = 1.887458609 + 2.75 Combine like terms: 1.887458609 + 2.75 = 4.637458609 y = 4.637458609 Simplifying y = 4.637458609

Subproblem 2

y + -2.75 = -1.887458609 Simplifying y + -2.75 = -1.887458609 Reorder the terms: -2.75 + y = -1.887458609 Solving -2.75 + y = -1.887458609 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + y = -1.887458609 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + y = -1.887458609 + 2.75 y = -1.887458609 + 2.75 Combine like terms: -1.887458609 + 2.75 = 0.862541391 y = 0.862541391 Simplifying y = 0.862541391

Solution

The solution to the problem is based on the solutions from the subproblems. y = {4.637458609, 0.862541391}

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