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Simplifying 3b2 + -37b + -90 = 0 Reorder the terms: -90 + -37b + 3b2 = 0 Solving -90 + -37b + 3b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -30 + -12.33333333b + b2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + -12.33333333b + 30 + b2 = 0 + 30 Reorder the terms: -30 + 30 + -12.33333333b + b2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -12.33333333b + b2 = 0 + 30 -12.33333333b + b2 = 0 + 30 Combine like terms: 0 + 30 = 30 -12.33333333b + b2 = 30 The b term is -12.33333333b. Take half its coefficient (-6.166666665). Square it (38.02777776) and add it to both sides. Add '38.02777776' to each side of the equation. -12.33333333b + 38.02777776 + b2 = 30 + 38.02777776 Reorder the terms: 38.02777776 + -12.33333333b + b2 = 30 + 38.02777776 Combine like terms: 30 + 38.02777776 = 68.02777776 38.02777776 + -12.33333333b + b2 = 68.02777776 Factor a perfect square on the left side: (b + -6.166666665)(b + -6.166666665) = 68.02777776 Calculate the square root of the right side: 8.247895353 Break this problem into two subproblems by setting (b + -6.166666665) equal to 8.247895353 and -8.247895353.Subproblem 1
b + -6.166666665 = 8.247895353 Simplifying b + -6.166666665 = 8.247895353 Reorder the terms: -6.166666665 + b = 8.247895353 Solving -6.166666665 + b = 8.247895353 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '6.166666665' to each side of the equation. -6.166666665 + 6.166666665 + b = 8.247895353 + 6.166666665 Combine like terms: -6.166666665 + 6.166666665 = 0.000000000 0.000000000 + b = 8.247895353 + 6.166666665 b = 8.247895353 + 6.166666665 Combine like terms: 8.247895353 + 6.166666665 = 14.414562018 b = 14.414562018 Simplifying b = 14.414562018Subproblem 2
b + -6.166666665 = -8.247895353 Simplifying b + -6.166666665 = -8.247895353 Reorder the terms: -6.166666665 + b = -8.247895353 Solving -6.166666665 + b = -8.247895353 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '6.166666665' to each side of the equation. -6.166666665 + 6.166666665 + b = -8.247895353 + 6.166666665 Combine like terms: -6.166666665 + 6.166666665 = 0.000000000 0.000000000 + b = -8.247895353 + 6.166666665 b = -8.247895353 + 6.166666665 Combine like terms: -8.247895353 + 6.166666665 = -2.081228688 b = -2.081228688 Simplifying b = -2.081228688Solution
The solution to the problem is based on the solutions from the subproblems. b = {14.414562018, -2.081228688}
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