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Simplifying 2b * b + -20b = 40.32 Multiply b * b 2b2 + -20b = 40.32 Reorder the terms: -20b + 2b2 = 40.32 Solving -20b + 2b2 = 40.32 Solving for variable 'b'. Reorder the terms: -40.32 + -20b + 2b2 = 40.32 + -40.32 Combine like terms: 40.32 + -40.32 = 0.00 -40.32 + -20b + 2b2 = 0.00 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -20.16 + -10b + b2 = 0.00 Move the constant term to the right: Add '20.16' to each side of the equation. -20.16 + -10b + 20.16 + b2 = 0.00 + 20.16 Reorder the terms: -20.16 + 20.16 + -10b + b2 = 0.00 + 20.16 Combine like terms: -20.16 + 20.16 = 0.00 0.00 + -10b + b2 = 0.00 + 20.16 -10b + b2 = 0.00 + 20.16 Combine like terms: 0.00 + 20.16 = 20.16 -10b + b2 = 20.16 The b term is -10b. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10b + 25 + b2 = 20.16 + 25 Reorder the terms: 25 + -10b + b2 = 20.16 + 25 Combine like terms: 20.16 + 25 = 45.16 25 + -10b + b2 = 45.16 Factor a perfect square on the left side: (b + -5)(b + -5) = 45.16 Calculate the square root of the right side: 6.720119047 Break this problem into two subproblems by setting (b + -5) equal to 6.720119047 and -6.720119047.Subproblem 1
b + -5 = 6.720119047 Simplifying b + -5 = 6.720119047 Reorder the terms: -5 + b = 6.720119047 Solving -5 + b = 6.720119047 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + b = 6.720119047 + 5 Combine like terms: -5 + 5 = 0 0 + b = 6.720119047 + 5 b = 6.720119047 + 5 Combine like terms: 6.720119047 + 5 = 11.720119047 b = 11.720119047 Simplifying b = 11.720119047Subproblem 2
b + -5 = -6.720119047 Simplifying b + -5 = -6.720119047 Reorder the terms: -5 + b = -6.720119047 Solving -5 + b = -6.720119047 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + b = -6.720119047 + 5 Combine like terms: -5 + 5 = 0 0 + b = -6.720119047 + 5 b = -6.720119047 + 5 Combine like terms: -6.720119047 + 5 = -1.720119047 b = -1.720119047 Simplifying b = -1.720119047Solution
The solution to the problem is based on the solutions from the subproblems. b = {11.720119047, -1.720119047}
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