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Simplifying 6b3 + -39b2 + -63b = 0 Reorder the terms: -63b + -39b2 + 6b3 = 0 Solving -63b + -39b2 + 6b3 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '3b'. 3b(-21 + -13b + 2b2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'b' equal to zero and attempt to solve: Simplifying b = 0 Solving b = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b = 0Subproblem 2
Set the factor '(-21 + -13b + 2b2)' equal to zero and attempt to solve: Simplifying -21 + -13b + 2b2 = 0 Solving -21 + -13b + 2b2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10.5 + -6.5b + b2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + -6.5b + 10.5 + b2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + -6.5b + b2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + -6.5b + b2 = 0 + 10.5 -6.5b + b2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 -6.5b + b2 = 10.5 The b term is -6.5b. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5b + 10.5625 + b2 = 10.5 + 10.5625 Reorder the terms: 10.5625 + -6.5b + b2 = 10.5 + 10.5625 Combine like terms: 10.5 + 10.5625 = 21.0625 10.5625 + -6.5b + b2 = 21.0625 Factor a perfect square on the left side: (b + -3.25)(b + -3.25) = 21.0625 Calculate the square root of the right side: 4.589389938 Break this problem into two subproblems by setting (b + -3.25) equal to 4.589389938 and -4.589389938.Subproblem 1
b + -3.25 = 4.589389938 Simplifying b + -3.25 = 4.589389938 Reorder the terms: -3.25 + b = 4.589389938 Solving -3.25 + b = 4.589389938 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + b = 4.589389938 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + b = 4.589389938 + 3.25 b = 4.589389938 + 3.25 Combine like terms: 4.589389938 + 3.25 = 7.839389938 b = 7.839389938 Simplifying b = 7.839389938Subproblem 2
b + -3.25 = -4.589389938 Simplifying b + -3.25 = -4.589389938 Reorder the terms: -3.25 + b = -4.589389938 Solving -3.25 + b = -4.589389938 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + b = -4.589389938 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + b = -4.589389938 + 3.25 b = -4.589389938 + 3.25 Combine like terms: -4.589389938 + 3.25 = -1.339389938 b = -1.339389938 Simplifying b = -1.339389938Solution
The solution to the problem is based on the solutions from the subproblems. b = {7.839389938, -1.339389938}Solution
b = {0, 7.839389938, -1.339389938}
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