b(20b-33)-2=0

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Solution for b(20b-33)-2=0 equation:


Simplifying
b(20b + -33) + -2 = 0

Reorder the terms:
b(-33 + 20b) + -2 = 0
(-33 * b + 20b * b) + -2 = 0
(-33b + 20b2) + -2 = 0

Reorder the terms:
-2 + -33b + 20b2 = 0

Solving
-2 + -33b + 20b2 = 0

Solving for variable 'b'.

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

Divide each side by '20'.
-0.1 + -1.65b + b2 = 0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + -1.65b + 0.1 + b2 = 0 + 0.1

Reorder the terms:
-0.1 + 0.1 + -1.65b + b2 = 0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + -1.65b + b2 = 0 + 0.1
-1.65b + b2 = 0 + 0.1

Combine like terms: 0 + 0.1 = 0.1
-1.65b + b2 = 0.1

The b term is -1.65b.  Take half its coefficient (-0.825).
Square it (0.680625) and add it to both sides.

Add '0.680625' to each side of the equation.
-1.65b + 0.680625 + b2 = 0.1 + 0.680625

Reorder the terms:
0.680625 + -1.65b + b2 = 0.1 + 0.680625

Combine like terms: 0.1 + 0.680625 = 0.780625
0.680625 + -1.65b + b2 = 0.780625

Factor a perfect square on the left side:
(b + -0.825)(b + -0.825) = 0.780625

Calculate the square root of the right side: 0.883529852

Break this problem into two subproblems by setting 
(b + -0.825) equal to 0.883529852 and -0.883529852.

Subproblem 1

b + -0.825 = 0.883529852 Simplifying b + -0.825 = 0.883529852 Reorder the terms: -0.825 + b = 0.883529852 Solving -0.825 + b = 0.883529852 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.825' to each side of the equation. -0.825 + 0.825 + b = 0.883529852 + 0.825 Combine like terms: -0.825 + 0.825 = 0.000 0.000 + b = 0.883529852 + 0.825 b = 0.883529852 + 0.825 Combine like terms: 0.883529852 + 0.825 = 1.708529852 b = 1.708529852 Simplifying b = 1.708529852

Subproblem 2

b + -0.825 = -0.883529852 Simplifying b + -0.825 = -0.883529852 Reorder the terms: -0.825 + b = -0.883529852 Solving -0.825 + b = -0.883529852 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.825' to each side of the equation. -0.825 + 0.825 + b = -0.883529852 + 0.825 Combine like terms: -0.825 + 0.825 = 0.000 0.000 + b = -0.883529852 + 0.825 b = -0.883529852 + 0.825 Combine like terms: -0.883529852 + 0.825 = -0.058529852 b = -0.058529852 Simplifying b = -0.058529852

Solution

The solution to the problem is based on the solutions from the subproblems. b = {1.708529852, -0.058529852}

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