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Simplifying -3b[b + -8] + -5 = 9[b + 2] + 1 Reorder the terms: -3b[-8 + b] + -5 = 9[b + 2] + 1 [-8 * -3b + b * -3b] + -5 = 9[b + 2] + 1 [24b + -3b2] + -5 = 9[b + 2] + 1 Reorder the terms: -5 + 24b + -3b2 = 9[b + 2] + 1 Reorder the terms: -5 + 24b + -3b2 = 9[2 + b] + 1 -5 + 24b + -3b2 = [2 * 9 + b * 9] + 1 -5 + 24b + -3b2 = [18 + 9b] + 1 Reorder the terms: -5 + 24b + -3b2 = 18 + 1 + 9b Combine like terms: 18 + 1 = 19 -5 + 24b + -3b2 = 19 + 9b Solving -5 + 24b + -3b2 = 19 + 9b Solving for variable 'b'. Reorder the terms: -5 + -19 + 24b + -9b + -3b2 = 19 + 9b + -19 + -9b Combine like terms: -5 + -19 = -24 -24 + 24b + -9b + -3b2 = 19 + 9b + -19 + -9b Combine like terms: 24b + -9b = 15b -24 + 15b + -3b2 = 19 + 9b + -19 + -9b Reorder the terms: -24 + 15b + -3b2 = 19 + -19 + 9b + -9b Combine like terms: 19 + -19 = 0 -24 + 15b + -3b2 = 0 + 9b + -9b -24 + 15b + -3b2 = 9b + -9b Combine like terms: 9b + -9b = 0 -24 + 15b + -3b2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-8 + 5b + -1b2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-8 + 5b + -1b2)' equal to zero and attempt to solve: Simplifying -8 + 5b + -1b2 = 0 Solving -8 + 5b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 8 + -5b + b2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -5b + -8 + b2 = 0 + -8 Reorder the terms: 8 + -8 + -5b + b2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5b + b2 = 0 + -8 -5b + b2 = 0 + -8 Combine like terms: 0 + -8 = -8 -5b + b2 = -8 The b term is -5b. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5b + 6.25 + b2 = -8 + 6.25 Reorder the terms: 6.25 + -5b + b2 = -8 + 6.25 Combine like terms: -8 + 6.25 = -1.75 6.25 + -5b + b2 = -1.75 Factor a perfect square on the left side: (b + -2.5)(b + -2.5) = -1.75 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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