4y^2-72y+36=

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Solution for 4y^2-72y+36= equation: 


Simplifying
4y2 + -72y + 36 = 0

Reorder the terms:
36 + -72y + 4y2 = 0

Solving
36 + -72y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(9 + -18y + y2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(9 + -18y + y2)' equal to zero and attempt to solve:

Simplifying
9 + -18y + y2 = 0

Solving
9 + -18y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -18y + -9 + y2 = 0 + -9

Reorder the terms:
9 + -9 + -18y + y2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -18y + y2 = 0 + -9
-18y + y2 = 0 + -9

Combine like terms: 0 + -9 = -9
-18y + y2 = -9

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 = -9 + 81

Reorder the terms:
81 + -18y + y2 = -9 + 81

Combine like terms: -9 + 81 = 72
81 + -18y + y2 = 72

Factor a perfect square on the left side:
(y + -9)(y + -9) = 72

Calculate the square root of the right side: 8.485281374

Break this problem into two subproblems by setting 
(y + -9) equal to 8.485281374 and -8.485281374.


Subproblem 1
y + -9 = 8.485281374

Simplifying
y + -9 = 8.485281374

Reorder the terms:
-9 + y = 8.485281374

Solving
-9 + y = 8.485281374

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 = 8.485281374 + 9

Combine like terms: -9 + 9 = 0
0 + y = 8.485281374 + 9
y = 8.485281374 + 9

Combine like terms: 8.485281374 + 9 = 17.485281374
y = 17.485281374

Simplifying
y = 17.485281374


Subproblem 2
y + -9 = -8.485281374

Simplifying
y + -9 = -8.485281374

Reorder the terms:
-9 + y = -8.485281374

Solving
-9 + y = -8.485281374

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 = -8.485281374 + 9

Combine like terms: -9 + 9 = 0
0 + y = -8.485281374 + 9
y = -8.485281374 + 9

Combine like terms: -8.485281374 + 9 = 0.514718626
y = 0.514718626

Simplifying
y = 0.514718626


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {17.485281374, 0.514718626}
Solution
y = {17.485281374, 0.514718626}

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