b^2+5b-35=33b

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Solution for b^2+5b-35=33b equation:


Simplifying
b2 + 5b + -35 = 33b

Reorder the terms:
-35 + 5b + b2 = 33b

Solving
-35 + 5b + b2 = 33b

Solving for variable 'b'.

Reorder the terms:
-35 + 5b + -33b + b2 = 33b + -33b

Combine like terms: 5b + -33b = -28b
-35 + -28b + b2 = 33b + -33b

Combine like terms: 33b + -33b = 0
-35 + -28b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + -28b + 35 + b2 = 0 + 35

Reorder the terms:
-35 + 35 + -28b + b2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -28b + b2 = 0 + 35
-28b + b2 = 0 + 35

Combine like terms: 0 + 35 = 35
-28b + b2 = 35

The b term is -28b.  Take half its coefficient (-14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
-28b + 196 + b2 = 35 + 196

Reorder the terms:
196 + -28b + b2 = 35 + 196

Combine like terms: 35 + 196 = 231
196 + -28b + b2 = 231

Factor a perfect square on the left side:
(b + -14)(b + -14) = 231

Calculate the square root of the right side: 15.198684154

Break this problem into two subproblems by setting 
(b + -14) equal to 15.198684154 and -15.198684154.

Subproblem 1

b + -14 = 15.198684154 Simplifying b + -14 = 15.198684154 Reorder the terms: -14 + b = 15.198684154 Solving -14 + b = 15.198684154 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + b = 15.198684154 + 14 Combine like terms: -14 + 14 = 0 0 + b = 15.198684154 + 14 b = 15.198684154 + 14 Combine like terms: 15.198684154 + 14 = 29.198684154 b = 29.198684154 Simplifying b = 29.198684154

Subproblem 2

b + -14 = -15.198684154 Simplifying b + -14 = -15.198684154 Reorder the terms: -14 + b = -15.198684154 Solving -14 + b = -15.198684154 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + b = -15.198684154 + 14 Combine like terms: -14 + 14 = 0 0 + b = -15.198684154 + 14 b = -15.198684154 + 14 Combine like terms: -15.198684154 + 14 = -1.198684154 b = -1.198684154 Simplifying b = -1.198684154

Solution

The solution to the problem is based on the solutions from the subproblems. b = {29.198684154, -1.198684154}

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