2y^2-36y+56=0

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Solution for 2y^2-36y+56=0 equation: 


Simplifying
2y2 + -36y + 56 = 0

Reorder the terms:
56 + -36y + 2y2 = 0

Solving
56 + -36y + 2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(28 + -18y + y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(28 + -18y + y2)' equal to zero and attempt to solve:

Simplifying
28 + -18y + y2 = 0

Solving
28 + -18y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + -18y + -28 + y2 = 0 + -28

Reorder the terms:
28 + -28 + -18y + y2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -18y + y2 = 0 + -28
-18y + y2 = 0 + -28

Combine like terms: 0 + -28 = -28
-18y + y2 = -28

The y term is -18y.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18y + 81 + y2 = -28 + 81

Reorder the terms:
81 + -18y + y2 = -28 + 81

Combine like terms: -28 + 81 = 53
81 + -18y + y2 = 53

Factor a perfect square on the left side:
(y + -9)(y + -9) = 53

Calculate the square root of the right side: 7.280109889

Break this problem into two subproblems by setting 
(y + -9) equal to 7.280109889 and -7.280109889.


Subproblem 1
y + -9 = 7.280109889

Simplifying
y + -9 = 7.280109889

Reorder the terms:
-9 + y = 7.280109889

Solving
-9 + y = 7.280109889

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '9' to each side of the equation.
-9 + 9 + y = 7.280109889 + 9

Combine like terms: -9 + 9 = 0
0 + y = 7.280109889 + 9
y = 7.280109889 + 9

Combine like terms: 7.280109889 + 9 = 16.280109889
y = 16.280109889

Simplifying
y = 16.280109889


Subproblem 2
y + -9 = -7.280109889

Simplifying
y + -9 = -7.280109889

Reorder the terms:
-9 + y = -7.280109889

Solving
-9 + y = -7.280109889

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '9' to each side of the equation.
-9 + 9 + y = -7.280109889 + 9

Combine like terms: -9 + 9 = 0
0 + y = -7.280109889 + 9
y = -7.280109889 + 9

Combine like terms: -7.280109889 + 9 = 1.719890111
y = 1.719890111

Simplifying
y = 1.719890111


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {16.280109889, 1.719890111}
Solution
y = {16.280109889, 1.719890111}

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