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Simplifying 2(3b + -2) + -5b = 4b(b + -1) + 8b Reorder the terms: 2(-2 + 3b) + -5b = 4b(b + -1) + 8b (-2 * 2 + 3b * 2) + -5b = 4b(b + -1) + 8b (-4 + 6b) + -5b = 4b(b + -1) + 8b Combine like terms: 6b + -5b = 1b -4 + 1b = 4b(b + -1) + 8b Reorder the terms: -4 + 1b = 4b(-1 + b) + 8b -4 + 1b = (-1 * 4b + b * 4b) + 8b -4 + 1b = (-4b + 4b2) + 8b Reorder the terms: -4 + 1b = -4b + 8b + 4b2 Combine like terms: -4b + 8b = 4b -4 + 1b = 4b + 4b2 Solving -4 + 1b = 4b + 4b2 Solving for variable 'b'. Combine like terms: 1b + -4b = -3b -4 + -3b + -4b2 = 4b + 4b2 + -4b + -4b2 Reorder the terms: -4 + -3b + -4b2 = 4b + -4b + 4b2 + -4b2 Combine like terms: 4b + -4b = 0 -4 + -3b + -4b2 = 0 + 4b2 + -4b2 -4 + -3b + -4b2 = 4b2 + -4b2 Combine like terms: 4b2 + -4b2 = 0 -4 + -3b + -4b2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 3b + 4b2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 3b + 4b2)' equal to zero and attempt to solve: Simplifying 4 + 3b + 4b2 = 0 Solving 4 + 3b + 4b2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1 + 0.75b + b2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 0.75b + -1 + b2 = 0 + -1 Reorder the terms: 1 + -1 + 0.75b + b2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 0.75b + b2 = 0 + -1 0.75b + b2 = 0 + -1 Combine like terms: 0 + -1 = -1 0.75b + b2 = -1 The b term is 0.75b. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75b + 0.140625 + b2 = -1 + 0.140625 Reorder the terms: 0.140625 + 0.75b + b2 = -1 + 0.140625 Combine like terms: -1 + 0.140625 = -0.859375 0.140625 + 0.75b + b2 = -0.859375 Factor a perfect square on the left side: (b + 0.375)(b + 0.375) = -0.859375 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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