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Simplifying 4b2 + 16b + 15 = (2b + -5) Reorder the terms: 15 + 16b + 4b2 = (2b + -5) Reorder the terms: 15 + 16b + 4b2 = (-5 + 2b) Remove parenthesis around (-5 + 2b) 15 + 16b + 4b2 = -5 + 2b Solving 15 + 16b + 4b2 = -5 + 2b Solving for variable 'b'. Reorder the terms: 15 + 5 + 16b + -2b + 4b2 = -5 + 2b + 5 + -2b Combine like terms: 15 + 5 = 20 20 + 16b + -2b + 4b2 = -5 + 2b + 5 + -2b Combine like terms: 16b + -2b = 14b 20 + 14b + 4b2 = -5 + 2b + 5 + -2b Reorder the terms: 20 + 14b + 4b2 = -5 + 5 + 2b + -2b Combine like terms: -5 + 5 = 0 20 + 14b + 4b2 = 0 + 2b + -2b 20 + 14b + 4b2 = 2b + -2b Combine like terms: 2b + -2b = 0 20 + 14b + 4b2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(10 + 7b + 2b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(10 + 7b + 2b2)' equal to zero and attempt to solve: Simplifying 10 + 7b + 2b2 = 0 Solving 10 + 7b + 2b2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5 + 3.5b + b2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 3.5b + -5 + b2 = 0 + -5 Reorder the terms: 5 + -5 + 3.5b + b2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3.5b + b2 = 0 + -5 3.5b + b2 = 0 + -5 Combine like terms: 0 + -5 = -5 3.5b + b2 = -5 The b term is 3.5b. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5b + 3.0625 + b2 = -5 + 3.0625 Reorder the terms: 3.0625 + 3.5b + b2 = -5 + 3.0625 Combine like terms: -5 + 3.0625 = -1.9375 3.0625 + 3.5b + b2 = -1.9375 Factor a perfect square on the left side: (b + 1.75)(b + 1.75) = -1.9375 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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