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Simplifying (5b + -5) + -2b(2b + 4) = 7 Reorder the terms: (-5 + 5b) + -2b(2b + 4) = 7 Remove parenthesis around (-5 + 5b) -5 + 5b + -2b(2b + 4) = 7 Reorder the terms: -5 + 5b + -2b(4 + 2b) = 7 -5 + 5b + (4 * -2b + 2b * -2b) = 7 -5 + 5b + (-8b + -4b2) = 7 Combine like terms: 5b + -8b = -3b -5 + -3b + -4b2 = 7 Solving -5 + -3b + -4b2 = 7 Solving for variable 'b'. Reorder the terms: -5 + -7 + -3b + -4b2 = 7 + -7 Combine like terms: -5 + -7 = -12 -12 + -3b + -4b2 = 7 + -7 Combine like terms: 7 + -7 = 0 -12 + -3b + -4b2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 3b + 4b2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + 3b + 4b2)' equal to zero and attempt to solve: Simplifying 12 + 3b + 4b2 = 0 Solving 12 + 3b + 4b2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3 + 0.75b + b2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 0.75b + -3 + b2 = 0 + -3 Reorder the terms: 3 + -3 + 0.75b + b2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 0.75b + b2 = 0 + -3 0.75b + b2 = 0 + -3 Combine like terms: 0 + -3 = -3 0.75b + b2 = -3 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 = -3 + 0.140625 Reorder the terms: 0.140625 + 0.75b + b2 = -3 + 0.140625 Combine like terms: -3 + 0.140625 = -2.859375 0.140625 + 0.75b + b2 = -2.859375 Factor a perfect square on the left side: (b + 0.375)(b + 0.375) = -2.859375 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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