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Simplifying 10b2 + -20b + -60 = 6 Reorder the terms: -60 + -20b + 10b2 = 6 Solving -60 + -20b + 10b2 = 6 Solving for variable 'b'. Reorder the terms: -60 + -6 + -20b + 10b2 = 6 + -6 Combine like terms: -60 + -6 = -66 -66 + -20b + 10b2 = 6 + -6 Combine like terms: 6 + -6 = 0 -66 + -20b + 10b2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-33 + -10b + 5b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-33 + -10b + 5b2)' equal to zero and attempt to solve: Simplifying -33 + -10b + 5b2 = 0 Solving -33 + -10b + 5b2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6.6 + -2b + b2 = 0 Move the constant term to the right: Add '6.6' to each side of the equation. -6.6 + -2b + 6.6 + b2 = 0 + 6.6 Reorder the terms: -6.6 + 6.6 + -2b + b2 = 0 + 6.6 Combine like terms: -6.6 + 6.6 = 0.0 0.0 + -2b + b2 = 0 + 6.6 -2b + b2 = 0 + 6.6 Combine like terms: 0 + 6.6 = 6.6 -2b + b2 = 6.6 The b term is -2b. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2b + 1 + b2 = 6.6 + 1 Reorder the terms: 1 + -2b + b2 = 6.6 + 1 Combine like terms: 6.6 + 1 = 7.6 1 + -2b + b2 = 7.6 Factor a perfect square on the left side: (b + -1)(b + -1) = 7.6 Calculate the square root of the right side: 2.75680975 Break this problem into two subproblems by setting (b + -1) equal to 2.75680975 and -2.75680975.Subproblem 1
b + -1 = 2.75680975 Simplifying b + -1 = 2.75680975 Reorder the terms: -1 + b = 2.75680975 Solving -1 + b = 2.75680975 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + b = 2.75680975 + 1 Combine like terms: -1 + 1 = 0 0 + b = 2.75680975 + 1 b = 2.75680975 + 1 Combine like terms: 2.75680975 + 1 = 3.75680975 b = 3.75680975 Simplifying b = 3.75680975Subproblem 2
b + -1 = -2.75680975 Simplifying b + -1 = -2.75680975 Reorder the terms: -1 + b = -2.75680975 Solving -1 + b = -2.75680975 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + b = -2.75680975 + 1 Combine like terms: -1 + 1 = 0 0 + b = -2.75680975 + 1 b = -2.75680975 + 1 Combine like terms: -2.75680975 + 1 = -1.75680975 b = -1.75680975 Simplifying b = -1.75680975Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.75680975, -1.75680975}Solution
b = {3.75680975, -1.75680975}
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