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Simplifying -2b(b + -10) = 2(10 + 5b) Reorder the terms: -2b(-10 + b) = 2(10 + 5b) (-10 * -2b + b * -2b) = 2(10 + 5b) (20b + -2b2) = 2(10 + 5b) 20b + -2b2 = (10 * 2 + 5b * 2) 20b + -2b2 = (20 + 10b) Solving 20b + -2b2 = 20 + 10b Solving for variable 'b'. Reorder the terms: -20 + 20b + -10b + -2b2 = 20 + 10b + -20 + -10b Combine like terms: 20b + -10b = 10b -20 + 10b + -2b2 = 20 + 10b + -20 + -10b Reorder the terms: -20 + 10b + -2b2 = 20 + -20 + 10b + -10b Combine like terms: 20 + -20 = 0 -20 + 10b + -2b2 = 0 + 10b + -10b -20 + 10b + -2b2 = 10b + -10b Combine like terms: 10b + -10b = 0 -20 + 10b + -2b2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + 5b + -1b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + 5b + -1b2)' equal to zero and attempt to solve: Simplifying -10 + 5b + -1b2 = 0 Solving -10 + 5b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 10 + -5b + b2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -5b + -10 + b2 = 0 + -10 Reorder the terms: 10 + -10 + -5b + b2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -5b + b2 = 0 + -10 -5b + b2 = 0 + -10 Combine like terms: 0 + -10 = -10 -5b + b2 = -10 The b term is -5b. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5b + 6.25 + b2 = -10 + 6.25 Reorder the terms: 6.25 + -5b + b2 = -10 + 6.25 Combine like terms: -10 + 6.25 = -3.75 6.25 + -5b + b2 = -3.75 Factor a perfect square on the left side: (b + -2.5)(b + -2.5) = -3.75 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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