3b^2-60b+36=0

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Solution for 3b^2-60b+36=0 equation: 


Simplifying
3b2 + -60b + 36 = 0

Reorder the terms:
36 + -60b + 3b2 = 0

Solving
36 + -60b + 3b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + -20b + b2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(12 + -20b + b2)' equal to zero and attempt to solve:

Simplifying
12 + -20b + b2 = 0

Solving
12 + -20b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -20b + -12 + b2 = 0 + -12

Reorder the terms:
12 + -12 + -20b + b2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -20b + b2 = 0 + -12
-20b + b2 = 0 + -12

Combine like terms: 0 + -12 = -12
-20b + b2 = -12

The b term is -20b.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20b + 100 + b2 = -12 + 100

Reorder the terms:
100 + -20b + b2 = -12 + 100

Combine like terms: -12 + 100 = 88
100 + -20b + b2 = 88

Factor a perfect square on the left side:
(b + -10)(b + -10) = 88

Calculate the square root of the right side: 9.38083152

Break this problem into two subproblems by setting 
(b + -10) equal to 9.38083152 and -9.38083152.


Subproblem 1
b + -10 = 9.38083152

Simplifying
b + -10 = 9.38083152

Reorder the terms:
-10 + b = 9.38083152

Solving
-10 + b = 9.38083152

Solving for variable 'b'.

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

Add '10' to each side of the equation.
-10 + 10 + b = 9.38083152 + 10

Combine like terms: -10 + 10 = 0
0 + b = 9.38083152 + 10
b = 9.38083152 + 10

Combine like terms: 9.38083152 + 10 = 19.38083152
b = 19.38083152

Simplifying
b = 19.38083152


Subproblem 2
b + -10 = -9.38083152

Simplifying
b + -10 = -9.38083152

Reorder the terms:
-10 + b = -9.38083152

Solving
-10 + b = -9.38083152

Solving for variable 'b'.

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

Add '10' to each side of the equation.
-10 + 10 + b = -9.38083152 + 10

Combine like terms: -10 + 10 = 0
0 + b = -9.38083152 + 10
b = -9.38083152 + 10

Combine like terms: -9.38083152 + 10 = 0.61916848
b = 0.61916848

Simplifying
b = 0.61916848


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {19.38083152, 0.61916848}
Solution
b = {19.38083152, 0.61916848}

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