8b+9+4b-3b(-2b)-(-5b)=

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Solution for 8b+9+4b-3b(-2b)-(-5b)= equation:


Simplifying
8b + 9 + 4b + -3b(-2b) + -1(-5b) = 0

Remove parenthesis around (-2b)
8b + 9 + 4b + -3b * -2b + -1(-5b) = 0

Reorder the terms for easier multiplication:
8b + 9 + 4b + -3 * -2b * b + -1(-5b) = 0

Multiply -3 * -2
8b + 9 + 4b + 6b * b + -1(-5b) = 0

Multiply b * b
8b + 9 + 4b + 6b2 + -1(-5b) = 0

Remove parenthesis around (-5b)
8b + 9 + 4b + 6b2 + -1 * -5b = 0

Multiply -1 * -5
8b + 9 + 4b + 6b2 + 5b = 0

Reorder the terms:
9 + 8b + 4b + 5b + 6b2 = 0

Combine like terms: 8b + 4b = 12b
9 + 12b + 5b + 6b2 = 0

Combine like terms: 12b + 5b = 17b
9 + 17b + 6b2 = 0

Solving
9 + 17b + 6b2 = 0

Solving for variable 'b'.

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

Divide each side by '6'.
1.5 + 2.833333333b + b2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 2.833333333b + -1.5 + b2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 2.833333333b + b2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 2.833333333b + b2 = 0 + -1.5
2.833333333b + b2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
2.833333333b + b2 = -1.5

The b term is 2.833333333b.  Take half its coefficient (1.416666667).
Square it (2.006944445) and add it to both sides.

Add '2.006944445' to each side of the equation.
2.833333333b + 2.006944445 + b2 = -1.5 + 2.006944445

Reorder the terms:
2.006944445 + 2.833333333b + b2 = -1.5 + 2.006944445

Combine like terms: -1.5 + 2.006944445 = 0.506944445
2.006944445 + 2.833333333b + b2 = 0.506944445

Factor a perfect square on the left side:
(b + 1.416666667)(b + 1.416666667) = 0.506944445

Calculate the square root of the right side: 0.712000313

Break this problem into two subproblems by setting 
(b + 1.416666667) equal to 0.712000313 and -0.712000313.

Subproblem 1

b + 1.416666667 = 0.712000313 Simplifying b + 1.416666667 = 0.712000313 Reorder the terms: 1.416666667 + b = 0.712000313 Solving 1.416666667 + b = 0.712000313 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.416666667' to each side of the equation. 1.416666667 + -1.416666667 + b = 0.712000313 + -1.416666667 Combine like terms: 1.416666667 + -1.416666667 = 0.000000000 0.000000000 + b = 0.712000313 + -1.416666667 b = 0.712000313 + -1.416666667 Combine like terms: 0.712000313 + -1.416666667 = -0.704666354 b = -0.704666354 Simplifying b = -0.704666354

Subproblem 2

b + 1.416666667 = -0.712000313 Simplifying b + 1.416666667 = -0.712000313 Reorder the terms: 1.416666667 + b = -0.712000313 Solving 1.416666667 + b = -0.712000313 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.416666667' to each side of the equation. 1.416666667 + -1.416666667 + b = -0.712000313 + -1.416666667 Combine like terms: 1.416666667 + -1.416666667 = 0.000000000 0.000000000 + b = -0.712000313 + -1.416666667 b = -0.712000313 + -1.416666667 Combine like terms: -0.712000313 + -1.416666667 = -2.12866698 b = -2.12866698 Simplifying b = -2.12866698

Solution

The solution to the problem is based on the solutions from the subproblems. b = {-0.704666354, -2.12866698}

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