-3b^2-8b+5b-2+13b^2-10-3b^2-7b=

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Solution for -3b^2-8b+5b-2+13b^2-10-3b^2-7b= equation:


Simplifying
-3b2 + -8b + 5b + -2 + 13b2 + -10 + -3b2 + -7b = 0

Reorder the terms:
-2 + -10 + -8b + 5b + -7b + -3b2 + 13b2 + -3b2 = 0

Combine like terms: -2 + -10 = -12
-12 + -8b + 5b + -7b + -3b2 + 13b2 + -3b2 = 0

Combine like terms: -8b + 5b = -3b
-12 + -3b + -7b + -3b2 + 13b2 + -3b2 = 0

Combine like terms: -3b + -7b = -10b
-12 + -10b + -3b2 + 13b2 + -3b2 = 0

Combine like terms: -3b2 + 13b2 = 10b2
-12 + -10b + 10b2 + -3b2 = 0

Combine like terms: 10b2 + -3b2 = 7b2
-12 + -10b + 7b2 = 0

Solving
-12 + -10b + 7b2 = 0

Solving for variable 'b'.

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

Divide each side by '7'.
-1.714285714 + -1.428571429b + b2 = 0

Move the constant term to the right:

Add '1.714285714' to each side of the equation.
-1.714285714 + -1.428571429b + 1.714285714 + b2 = 0 + 1.714285714

Reorder the terms:
-1.714285714 + 1.714285714 + -1.428571429b + b2 = 0 + 1.714285714

Combine like terms: -1.714285714 + 1.714285714 = 0.000000000
0.000000000 + -1.428571429b + b2 = 0 + 1.714285714
-1.428571429b + b2 = 0 + 1.714285714

Combine like terms: 0 + 1.714285714 = 1.714285714
-1.428571429b + b2 = 1.714285714

The b term is -1.428571429b.  Take half its coefficient (-0.7142857145).
Square it (0.5102040819) and add it to both sides.

Add '0.5102040819' to each side of the equation.
-1.428571429b + 0.5102040819 + b2 = 1.714285714 + 0.5102040819

Reorder the terms:
0.5102040819 + -1.428571429b + b2 = 1.714285714 + 0.5102040819

Combine like terms: 1.714285714 + 0.5102040819 = 2.2244897959
0.5102040819 + -1.428571429b + b2 = 2.2244897959

Factor a perfect square on the left side:
(b + -0.7142857145)(b + -0.7142857145) = 2.2244897959

Calculate the square root of the right side: 1.491472358

Break this problem into two subproblems by setting 
(b + -0.7142857145) equal to 1.491472358 and -1.491472358.

Subproblem 1

b + -0.7142857145 = 1.491472358 Simplifying b + -0.7142857145 = 1.491472358 Reorder the terms: -0.7142857145 + b = 1.491472358 Solving -0.7142857145 + b = 1.491472358 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + b = 1.491472358 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + b = 1.491472358 + 0.7142857145 b = 1.491472358 + 0.7142857145 Combine like terms: 1.491472358 + 0.7142857145 = 2.2057580725 b = 2.2057580725 Simplifying b = 2.2057580725

Subproblem 2

b + -0.7142857145 = -1.491472358 Simplifying b + -0.7142857145 = -1.491472358 Reorder the terms: -0.7142857145 + b = -1.491472358 Solving -0.7142857145 + b = -1.491472358 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + b = -1.491472358 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + b = -1.491472358 + 0.7142857145 b = -1.491472358 + 0.7142857145 Combine like terms: -1.491472358 + 0.7142857145 = -0.7771866435 b = -0.7771866435 Simplifying b = -0.7771866435

Solution

The solution to the problem is based on the solutions from the subproblems. b = {2.2057580725, -0.7771866435}

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