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Simplifying -5b(2b + 4) + (11b + -5) = 0 Reorder the terms: -5b(4 + 2b) + (11b + -5) = 0 (4 * -5b + 2b * -5b) + (11b + -5) = 0 (-20b + -10b2) + (11b + -5) = 0 Reorder the terms: -20b + -10b2 + (-5 + 11b) = 0 Remove parenthesis around (-5 + 11b) -20b + -10b2 + -5 + 11b = 0 Reorder the terms: -5 + -20b + 11b + -10b2 = 0 Combine like terms: -20b + 11b = -9b -5 + -9b + -10b2 = 0 Solving -5 + -9b + -10b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 9b + 10b2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 9b + 10b2)' equal to zero and attempt to solve: Simplifying 5 + 9b + 10b2 = 0 Solving 5 + 9b + 10b2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.5 + 0.9b + b2 = 0.0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 0.9b + -0.5 + b2 = 0.0 + -0.5 Reorder the terms: 0.5 + -0.5 + 0.9b + b2 = 0.0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 0.9b + b2 = 0.0 + -0.5 0.9b + b2 = 0.0 + -0.5 Combine like terms: 0.0 + -0.5 = -0.5 0.9b + b2 = -0.5 The b term is 0.9b. Take half its coefficient (0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. 0.9b + 0.2025 + b2 = -0.5 + 0.2025 Reorder the terms: 0.2025 + 0.9b + b2 = -0.5 + 0.2025 Combine like terms: -0.5 + 0.2025 = -0.2975 0.2025 + 0.9b + b2 = -0.2975 Factor a perfect square on the left side: (b + 0.45)(b + 0.45) = -0.2975 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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