b^2-12b+12=0

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Solution for b^2-12b+12=0 equation:


Simplifying
b2 + -12b + 12 = 0

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

Solving
12 + -12b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The b term is -12b.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12b + 36 + b2 = -12 + 36

Reorder the terms:
36 + -12b + b2 = -12 + 36

Combine like terms: -12 + 36 = 24
36 + -12b + b2 = 24

Factor a perfect square on the left side:
(b + -6)(b + -6) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(b + -6) equal to 4.898979486 and -4.898979486.

Subproblem 1

b + -6 = 4.898979486 Simplifying b + -6 = 4.898979486 Reorder the terms: -6 + b = 4.898979486 Solving -6 + b = 4.898979486 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + b = 4.898979486 + 6 Combine like terms: -6 + 6 = 0 0 + b = 4.898979486 + 6 b = 4.898979486 + 6 Combine like terms: 4.898979486 + 6 = 10.898979486 b = 10.898979486 Simplifying b = 10.898979486

Subproblem 2

b + -6 = -4.898979486 Simplifying b + -6 = -4.898979486 Reorder the terms: -6 + b = -4.898979486 Solving -6 + b = -4.898979486 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + b = -4.898979486 + 6 Combine like terms: -6 + 6 = 0 0 + b = -4.898979486 + 6 b = -4.898979486 + 6 Combine like terms: -4.898979486 + 6 = 1.101020514 b = 1.101020514 Simplifying b = 1.101020514

Solution

The solution to the problem is based on the solutions from the subproblems. b = {10.898979486, 1.101020514}

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