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Simplifying 36 + -7b = -3b(8b + 5) Reorder the terms: 36 + -7b = -3b(5 + 8b) 36 + -7b = (5 * -3b + 8b * -3b) 36 + -7b = (-15b + -24b2) Solving 36 + -7b = -15b + -24b2 Solving for variable 'b'. Combine like terms: -7b + 15b = 8b 36 + 8b + 24b2 = -15b + -24b2 + 15b + 24b2 Reorder the terms: 36 + 8b + 24b2 = -15b + 15b + -24b2 + 24b2 Combine like terms: -15b + 15b = 0 36 + 8b + 24b2 = 0 + -24b2 + 24b2 36 + 8b + 24b2 = -24b2 + 24b2 Combine like terms: -24b2 + 24b2 = 0 36 + 8b + 24b2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(9 + 2b + 6b2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(9 + 2b + 6b2)' equal to zero and attempt to solve: Simplifying 9 + 2b + 6b2 = 0 Solving 9 + 2b + 6b2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.5 + 0.3333333333b + b2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 0.3333333333b + -1.5 + b2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 0.3333333333b + b2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 0.3333333333b + b2 = 0 + -1.5 0.3333333333b + b2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 0.3333333333b + b2 = -1.5 The b term is 0.3333333333b. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333b + 0.02777777779 + b2 = -1.5 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333b + b2 = -1.5 + 0.02777777779 Combine like terms: -1.5 + 0.02777777779 = -1.47222222221 0.02777777779 + 0.3333333333b + b2 = -1.47222222221 Factor a perfect square on the left side: (b + 0.1666666667)(b + 0.1666666667) = -1.47222222221 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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