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Simplifying 2b(5b + -9b) + -3b = 14 Combine like terms: 5b + -9b = -4b 2b(-4b) + -3b = 14 Remove parenthesis around (-4b) 2b * -4b + -3b = 14 Reorder the terms for easier multiplication: 2 * -4b * b + -3b = 14 Multiply 2 * -4 -8b * b + -3b = 14 Multiply b * b -8b2 + -3b = 14 Reorder the terms: -3b + -8b2 = 14 Solving -3b + -8b2 = 14 Solving for variable 'b'. Reorder the terms: -14 + -3b + -8b2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + -3b + -8b2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(14 + 3b + 8b2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(14 + 3b + 8b2)' equal to zero and attempt to solve: Simplifying 14 + 3b + 8b2 = 0 Solving 14 + 3b + 8b2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.75 + 0.375b + b2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + 0.375b + -1.75 + b2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + 0.375b + b2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + 0.375b + b2 = 0 + -1.75 0.375b + b2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 0.375b + b2 = -1.75 The b term is 0.375b. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375b + 0.03515625 + b2 = -1.75 + 0.03515625 Reorder the terms: 0.03515625 + 0.375b + b2 = -1.75 + 0.03515625 Combine like terms: -1.75 + 0.03515625 = -1.71484375 0.03515625 + 0.375b + b2 = -1.71484375 Factor a perfect square on the left side: (b + 0.1875)(b + 0.1875) = -1.71484375 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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