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Simplifying 2b + 1 = 2b2 + 4b + 6 Reorder the terms: 1 + 2b = 2b2 + 4b + 6 Reorder the terms: 1 + 2b = 6 + 4b + 2b2 Solving 1 + 2b = 6 + 4b + 2b2 Solving for variable 'b'. Reorder the terms: 1 + -6 + 2b + -4b + -2b2 = 6 + 4b + 2b2 + -6 + -4b + -2b2 Combine like terms: 1 + -6 = -5 -5 + 2b + -4b + -2b2 = 6 + 4b + 2b2 + -6 + -4b + -2b2 Combine like terms: 2b + -4b = -2b -5 + -2b + -2b2 = 6 + 4b + 2b2 + -6 + -4b + -2b2 Reorder the terms: -5 + -2b + -2b2 = 6 + -6 + 4b + -4b + 2b2 + -2b2 Combine like terms: 6 + -6 = 0 -5 + -2b + -2b2 = 0 + 4b + -4b + 2b2 + -2b2 -5 + -2b + -2b2 = 4b + -4b + 2b2 + -2b2 Combine like terms: 4b + -4b = 0 -5 + -2b + -2b2 = 0 + 2b2 + -2b2 -5 + -2b + -2b2 = 2b2 + -2b2 Combine like terms: 2b2 + -2b2 = 0 -5 + -2b + -2b2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 2b + 2b2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 2b + 2b2)' equal to zero and attempt to solve: Simplifying 5 + 2b + 2b2 = 0 Solving 5 + 2b + 2b2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + b + b2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + b + -2.5 + b2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + b + b2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b + b2 = 0 + -2.5 b + b2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 b + b2 = -2.5 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 = -2.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + b2 = -2.5 + 0.25 Combine like terms: -2.5 + 0.25 = -2.25 1.25 + b2 = -2.25 Factor a perfect square on the left side: (b + 0.5)(b + 0.5) = -2.25 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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