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Simplifying 30b + -5b(b + 10) = 142 Reorder the terms: 30b + -5b(10 + b) = 142 30b + (10 * -5b + b * -5b) = 142 30b + (-50b + -5b2) = 142 Combine like terms: 30b + -50b = -20b -20b + -5b2 = 142 Solving -20b + -5b2 = 142 Solving for variable 'b'. Reorder the terms: -142 + -20b + -5b2 = 142 + -142 Combine like terms: 142 + -142 = 0 -142 + -20b + -5b2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(142 + 20b + 5b2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(142 + 20b + 5b2)' equal to zero and attempt to solve: Simplifying 142 + 20b + 5b2 = 0 Solving 142 + 20b + 5b2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 28.4 + 4b + b2 = 0 Move the constant term to the right: Add '-28.4' to each side of the equation. 28.4 + 4b + -28.4 + b2 = 0 + -28.4 Reorder the terms: 28.4 + -28.4 + 4b + b2 = 0 + -28.4 Combine like terms: 28.4 + -28.4 = 0.0 0.0 + 4b + b2 = 0 + -28.4 4b + b2 = 0 + -28.4 Combine like terms: 0 + -28.4 = -28.4 4b + b2 = -28.4 The b term is 4b. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4b + 4 + b2 = -28.4 + 4 Reorder the terms: 4 + 4b + b2 = -28.4 + 4 Combine like terms: -28.4 + 4 = -24.4 4 + 4b + b2 = -24.4 Factor a perfect square on the left side: (b + 2)(b + 2) = -24.4 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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