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Simplifying -6b(3b + 4) + (19b + -3) = 0 Reorder the terms: -6b(4 + 3b) + (19b + -3) = 0 (4 * -6b + 3b * -6b) + (19b + -3) = 0 (-24b + -18b2) + (19b + -3) = 0 Reorder the terms: -24b + -18b2 + (-3 + 19b) = 0 Remove parenthesis around (-3 + 19b) -24b + -18b2 + -3 + 19b = 0 Reorder the terms: -3 + -24b + 19b + -18b2 = 0 Combine like terms: -24b + 19b = -5b -3 + -5b + -18b2 = 0 Solving -3 + -5b + -18b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 5b + 18b2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 5b + 18b2)' equal to zero and attempt to solve: Simplifying 3 + 5b + 18b2 = 0 Solving 3 + 5b + 18b2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.1666666667 + 0.2777777778b + b2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + 0.2777777778b + -0.1666666667 + b2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + 0.2777777778b + b2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + 0.2777777778b + b2 = 0 + -0.1666666667 0.2777777778b + b2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 0.2777777778b + b2 = -0.1666666667 The b term is 0.2777777778b. Take half its coefficient (0.1388888889). Square it (0.01929012346) and add it to both sides. Add '0.01929012346' to each side of the equation. 0.2777777778b + 0.01929012346 + b2 = -0.1666666667 + 0.01929012346 Reorder the terms: 0.01929012346 + 0.2777777778b + b2 = -0.1666666667 + 0.01929012346 Combine like terms: -0.1666666667 + 0.01929012346 = -0.14737654324 0.01929012346 + 0.2777777778b + b2 = -0.14737654324 Factor a perfect square on the left side: (b + 0.1388888889)(b + 0.1388888889) = -0.14737654324 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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