2(3b-4)8b-11=

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Solution for 2(3b-4)8b-11= equation:


Simplifying
2(3b + -4) * 8b + -11 = 0

Reorder the terms:
2(-4 + 3b) * 8b + -11 = 0

Reorder the terms for easier multiplication:
2 * 8b(-4 + 3b) + -11 = 0

Multiply 2 * 8
16b(-4 + 3b) + -11 = 0
(-4 * 16b + 3b * 16b) + -11 = 0
(-64b + 48b2) + -11 = 0

Reorder the terms:
-11 + -64b + 48b2 = 0

Solving
-11 + -64b + 48b2 = 0

Solving for variable 'b'.

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

Divide each side by '48'.
-0.2291666667 + -1.333333333b + b2 = 0

Move the constant term to the right:

Add '0.2291666667' to each side of the equation.
-0.2291666667 + -1.333333333b + 0.2291666667 + b2 = 0 + 0.2291666667

Reorder the terms:
-0.2291666667 + 0.2291666667 + -1.333333333b + b2 = 0 + 0.2291666667

Combine like terms: -0.2291666667 + 0.2291666667 = 0.0000000000
0.0000000000 + -1.333333333b + b2 = 0 + 0.2291666667
-1.333333333b + b2 = 0 + 0.2291666667

Combine like terms: 0 + 0.2291666667 = 0.2291666667
-1.333333333b + b2 = 0.2291666667

The b term is -1.333333333b.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333b + 0.4444444442 + b2 = 0.2291666667 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333b + b2 = 0.2291666667 + 0.4444444442

Combine like terms: 0.2291666667 + 0.4444444442 = 0.6736111109
0.4444444442 + -1.333333333b + b2 = 0.6736111109

Factor a perfect square on the left side:
(b + -0.6666666665)(b + -0.6666666665) = 0.6736111109

Calculate the square root of the right side: 0.82073815

Break this problem into two subproblems by setting 
(b + -0.6666666665) equal to 0.82073815 and -0.82073815.

Subproblem 1

b + -0.6666666665 = 0.82073815 Simplifying b + -0.6666666665 = 0.82073815 Reorder the terms: -0.6666666665 + b = 0.82073815 Solving -0.6666666665 + b = 0.82073815 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + b = 0.82073815 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + b = 0.82073815 + 0.6666666665 b = 0.82073815 + 0.6666666665 Combine like terms: 0.82073815 + 0.6666666665 = 1.4874048165 b = 1.4874048165 Simplifying b = 1.4874048165

Subproblem 2

b + -0.6666666665 = -0.82073815 Simplifying b + -0.6666666665 = -0.82073815 Reorder the terms: -0.6666666665 + b = -0.82073815 Solving -0.6666666665 + b = -0.82073815 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + b = -0.82073815 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + b = -0.82073815 + 0.6666666665 b = -0.82073815 + 0.6666666665 Combine like terms: -0.82073815 + 0.6666666665 = -0.1540714835 b = -0.1540714835 Simplifying b = -0.1540714835

Solution

The solution to the problem is based on the solutions from the subproblems. b = {1.4874048165, -0.1540714835}

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