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Simplifying -4b(1 + -9b + -2b2) = 0 (1 * -4b + -9b * -4b + -2b2 * -4b) = 0 (-4b + 36b2 + 8b3) = 0 Solving -4b + 36b2 + 8b3 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '4b'. 4b(-1 + 9b + 2b2) = 0 Ignore the factor 4.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 '(-1 + 9b + 2b2)' equal to zero and attempt to solve: Simplifying -1 + 9b + 2b2 = 0 Solving -1 + 9b + 2b2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + 4.5b + b2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 4.5b + 0.5 + b2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 4.5b + b2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 4.5b + b2 = 0 + 0.5 4.5b + b2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 4.5b + b2 = 0.5 The b term is 4.5b. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5b + 5.0625 + b2 = 0.5 + 5.0625 Reorder the terms: 5.0625 + 4.5b + b2 = 0.5 + 5.0625 Combine like terms: 0.5 + 5.0625 = 5.5625 5.0625 + 4.5b + b2 = 5.5625 Factor a perfect square on the left side: (b + 2.25)(b + 2.25) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (b + 2.25) equal to 2.358495283 and -2.358495283.Subproblem 1
b + 2.25 = 2.358495283 Simplifying b + 2.25 = 2.358495283 Reorder the terms: 2.25 + b = 2.358495283 Solving 2.25 + b = 2.358495283 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + b = 2.358495283 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + b = 2.358495283 + -2.25 b = 2.358495283 + -2.25 Combine like terms: 2.358495283 + -2.25 = 0.108495283 b = 0.108495283 Simplifying b = 0.108495283Subproblem 2
b + 2.25 = -2.358495283 Simplifying b + 2.25 = -2.358495283 Reorder the terms: 2.25 + b = -2.358495283 Solving 2.25 + b = -2.358495283 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + b = -2.358495283 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + b = -2.358495283 + -2.25 b = -2.358495283 + -2.25 Combine like terms: -2.358495283 + -2.25 = -4.608495283 b = -4.608495283 Simplifying b = -4.608495283Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.108495283, -4.608495283}Solution
b = {0, 0.108495283, -4.608495283}
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