(b^2-2b^2+b)-(b^2+3b-1)=

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Solution for (b^2-2b^2+b)-(b^2+3b-1)= equation:


Simplifying
(b2 + -2b2 + b) + -1(b2 + 3b + -1) = 0

Reorder the terms:
(b + b2 + -2b2) + -1(b2 + 3b + -1) = 0

Combine like terms: b2 + -2b2 = -1b2
(b + -1b2) + -1(b2 + 3b + -1) = 0

Remove parenthesis around (b + -1b2)
b + -1b2 + -1(b2 + 3b + -1) = 0

Reorder the terms:
b + -1b2 + -1(-1 + 3b + b2) = 0
b + -1b2 + (-1 * -1 + 3b * -1 + b2 * -1) = 0
b + -1b2 + (1 + -3b + -1b2) = 0

Reorder the terms:
1 + b + -3b + -1b2 + -1b2 = 0

Combine like terms: b + -3b = -2b
1 + -2b + -1b2 + -1b2 = 0

Combine like terms: -1b2 + -1b2 = -2b2
1 + -2b + -2b2 = 0

Solving
1 + -2b + -2b2 = 0

Solving for variable 'b'.

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-0.5 + b + b2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + b + 0.5 + b2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + b + b2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + b + b2 = 0 + 0.5
b + b2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
b + b2 = 0.5

The b term is b.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + b2 = 0.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + b2 = 0.5 + 0.25

Combine like terms: 0.5 + 0.25 = 0.75
1.25 + b2 = 0.75

Factor a perfect square on the left side:
(b + 0.5)(b + 0.5) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(b + 0.5) equal to 0.866025404 and -0.866025404.

Subproblem 1

b + 0.5 = 0.866025404 Simplifying b + 0.5 = 0.866025404 Reorder the terms: 0.5 + b = 0.866025404 Solving 0.5 + b = 0.866025404 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + b = 0.866025404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = 0.866025404 + -0.5 b = 0.866025404 + -0.5 Combine like terms: 0.866025404 + -0.5 = 0.366025404 b = 0.366025404 Simplifying b = 0.366025404

Subproblem 2

b + 0.5 = -0.866025404 Simplifying b + 0.5 = -0.866025404 Reorder the terms: 0.5 + b = -0.866025404 Solving 0.5 + b = -0.866025404 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + b = -0.866025404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = -0.866025404 + -0.5 b = -0.866025404 + -0.5 Combine like terms: -0.866025404 + -0.5 = -1.366025404 b = -1.366025404 Simplifying b = -1.366025404

Solution

The solution to the problem is based on the solutions from the subproblems. b = {0.366025404, -1.366025404}

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