2y^2-18.8y+33.76=0

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Solution for 2y^2-18.8y+33.76=0 equation:


Simplifying
2y2 + -18.8y + 33.76 = 0

Reorder the terms:
33.76 + -18.8y + 2y2 = 0

Solving
33.76 + -18.8y + 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'.
16.88 + -9.4y + y2 = 0

Move the constant term to the right:

Add '-16.88' to each side of the equation.
16.88 + -9.4y + -16.88 + y2 = 0 + -16.88

Reorder the terms:
16.88 + -16.88 + -9.4y + y2 = 0 + -16.88

Combine like terms: 16.88 + -16.88 = 0.00
0.00 + -9.4y + y2 = 0 + -16.88
-9.4y + y2 = 0 + -16.88

Combine like terms: 0 + -16.88 = -16.88
-9.4y + y2 = -16.88

The y term is -9.4y.  Take half its coefficient (-4.7).
Square it (22.09) and add it to both sides.

Add '22.09' to each side of the equation.
-9.4y + 22.09 + y2 = -16.88 + 22.09

Reorder the terms:
22.09 + -9.4y + y2 = -16.88 + 22.09

Combine like terms: -16.88 + 22.09 = 5.21
22.09 + -9.4y + y2 = 5.21

Factor a perfect square on the left side:
(y + -4.7)(y + -4.7) = 5.21

Calculate the square root of the right side: 2.282542442

Break this problem into two subproblems by setting 
(y + -4.7) equal to 2.282542442 and -2.282542442.

Subproblem 1

y + -4.7 = 2.282542442 Simplifying y + -4.7 = 2.282542442 Reorder the terms: -4.7 + y = 2.282542442 Solving -4.7 + y = 2.282542442 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.7' to each side of the equation. -4.7 + 4.7 + y = 2.282542442 + 4.7 Combine like terms: -4.7 + 4.7 = 0.0 0.0 + y = 2.282542442 + 4.7 y = 2.282542442 + 4.7 Combine like terms: 2.282542442 + 4.7 = 6.982542442 y = 6.982542442 Simplifying y = 6.982542442

Subproblem 2

y + -4.7 = -2.282542442 Simplifying y + -4.7 = -2.282542442 Reorder the terms: -4.7 + y = -2.282542442 Solving -4.7 + y = -2.282542442 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.7' to each side of the equation. -4.7 + 4.7 + y = -2.282542442 + 4.7 Combine like terms: -4.7 + 4.7 = 0.0 0.0 + y = -2.282542442 + 4.7 y = -2.282542442 + 4.7 Combine like terms: -2.282542442 + 4.7 = 2.417457558 y = 2.417457558 Simplifying y = 2.417457558

Solution

The solution to the problem is based on the solutions from the subproblems. y = {6.982542442, 2.417457558}

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