4y^2-33y+27=0

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Solution for 4y^2-33y+27=0 equation:


Simplifying
4y2 + -33y + 27 = 0

Reorder the terms:
27 + -33y + 4y2 = 0

Solving
27 + -33y + 4y2 = 0

Solving for variable 'y'.

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

Divide each side by '4'.
6.75 + -8.25y + y2 = 0

Move the constant term to the right:

Add '-6.75' to each side of the equation.
6.75 + -8.25y + -6.75 + y2 = 0 + -6.75

Reorder the terms:
6.75 + -6.75 + -8.25y + y2 = 0 + -6.75

Combine like terms: 6.75 + -6.75 = 0.00
0.00 + -8.25y + y2 = 0 + -6.75
-8.25y + y2 = 0 + -6.75

Combine like terms: 0 + -6.75 = -6.75
-8.25y + y2 = -6.75

The y term is -8.25y.  Take half its coefficient (-4.125).
Square it (17.015625) and add it to both sides.

Add '17.015625' to each side of the equation.
-8.25y + 17.015625 + y2 = -6.75 + 17.015625

Reorder the terms:
17.015625 + -8.25y + y2 = -6.75 + 17.015625

Combine like terms: -6.75 + 17.015625 = 10.265625
17.015625 + -8.25y + y2 = 10.265625

Factor a perfect square on the left side:
(y + -4.125)(y + -4.125) = 10.265625

Calculate the square root of the right side: 3.204001404

Break this problem into two subproblems by setting 
(y + -4.125) equal to 3.204001404 and -3.204001404.

Subproblem 1

y + -4.125 = 3.204001404 Simplifying y + -4.125 = 3.204001404 Reorder the terms: -4.125 + y = 3.204001404 Solving -4.125 + y = 3.204001404 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + y = 3.204001404 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + y = 3.204001404 + 4.125 y = 3.204001404 + 4.125 Combine like terms: 3.204001404 + 4.125 = 7.329001404 y = 7.329001404 Simplifying y = 7.329001404

Subproblem 2

y + -4.125 = -3.204001404 Simplifying y + -4.125 = -3.204001404 Reorder the terms: -4.125 + y = -3.204001404 Solving -4.125 + y = -3.204001404 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + y = -3.204001404 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + y = -3.204001404 + 4.125 y = -3.204001404 + 4.125 Combine like terms: -3.204001404 + 4.125 = 0.920998596 y = 0.920998596 Simplifying y = 0.920998596

Solution

The solution to the problem is based on the solutions from the subproblems. y = {7.329001404, 0.920998596}

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