36y^2-165y+25=0

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Solution for 36y^2-165y+25=0 equation:


Simplifying
36y2 + -165y + 25 = 0

Reorder the terms:
25 + -165y + 36y2 = 0

Solving
25 + -165y + 36y2 = 0

Solving for variable 'y'.

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

Divide each side by '36'.
0.6944444444 + -4.583333333y + y2 = 0

Move the constant term to the right:

Add '-0.6944444444' to each side of the equation.
0.6944444444 + -4.583333333y + -0.6944444444 + y2 = 0 + -0.6944444444

Reorder the terms:
0.6944444444 + -0.6944444444 + -4.583333333y + y2 = 0 + -0.6944444444

Combine like terms: 0.6944444444 + -0.6944444444 = 0.0000000000
0.0000000000 + -4.583333333y + y2 = 0 + -0.6944444444
-4.583333333y + y2 = 0 + -0.6944444444

Combine like terms: 0 + -0.6944444444 = -0.6944444444
-4.583333333y + y2 = -0.6944444444

The y term is -4.583333333y.  Take half its coefficient (-2.291666667).
Square it (5.251736113) and add it to both sides.

Add '5.251736113' to each side of the equation.
-4.583333333y + 5.251736113 + y2 = -0.6944444444 + 5.251736113

Reorder the terms:
5.251736113 + -4.583333333y + y2 = -0.6944444444 + 5.251736113

Combine like terms: -0.6944444444 + 5.251736113 = 4.5572916686
5.251736113 + -4.583333333y + y2 = 4.5572916686

Factor a perfect square on the left side:
(y + -2.291666667)(y + -2.291666667) = 4.5572916686

Calculate the square root of the right side: 2.13478141

Break this problem into two subproblems by setting 
(y + -2.291666667) equal to 2.13478141 and -2.13478141.

Subproblem 1

y + -2.291666667 = 2.13478141 Simplifying y + -2.291666667 = 2.13478141 Reorder the terms: -2.291666667 + y = 2.13478141 Solving -2.291666667 + y = 2.13478141 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.291666667' to each side of the equation. -2.291666667 + 2.291666667 + y = 2.13478141 + 2.291666667 Combine like terms: -2.291666667 + 2.291666667 = 0.000000000 0.000000000 + y = 2.13478141 + 2.291666667 y = 2.13478141 + 2.291666667 Combine like terms: 2.13478141 + 2.291666667 = 4.426448077 y = 4.426448077 Simplifying y = 4.426448077

Subproblem 2

y + -2.291666667 = -2.13478141 Simplifying y + -2.291666667 = -2.13478141 Reorder the terms: -2.291666667 + y = -2.13478141 Solving -2.291666667 + y = -2.13478141 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.291666667' to each side of the equation. -2.291666667 + 2.291666667 + y = -2.13478141 + 2.291666667 Combine like terms: -2.291666667 + 2.291666667 = 0.000000000 0.000000000 + y = -2.13478141 + 2.291666667 y = -2.13478141 + 2.291666667 Combine like terms: -2.13478141 + 2.291666667 = 0.156885257 y = 0.156885257 Simplifying y = 0.156885257

Solution

The solution to the problem is based on the solutions from the subproblems. y = {4.426448077, 0.156885257}

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