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Simplifying 16b3 + 62b2 + -72b = 0 Reorder the terms: -72b + 62b2 + 16b3 = 0 Solving -72b + 62b2 + 16b3 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2b'. 2b(-36 + 31b + 8b2) = 0 Ignore the factor 2.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 '(-36 + 31b + 8b2)' equal to zero and attempt to solve: Simplifying -36 + 31b + 8b2 = 0 Solving -36 + 31b + 8b2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4.5 + 3.875b + b2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 3.875b + 4.5 + b2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 3.875b + b2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 3.875b + b2 = 0 + 4.5 3.875b + b2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 3.875b + b2 = 4.5 The b term is 3.875b. Take half its coefficient (1.9375). Square it (3.75390625) and add it to both sides. Add '3.75390625' to each side of the equation. 3.875b + 3.75390625 + b2 = 4.5 + 3.75390625 Reorder the terms: 3.75390625 + 3.875b + b2 = 4.5 + 3.75390625 Combine like terms: 4.5 + 3.75390625 = 8.25390625 3.75390625 + 3.875b + b2 = 8.25390625 Factor a perfect square on the left side: (b + 1.9375)(b + 1.9375) = 8.25390625 Calculate the square root of the right side: 2.872961234 Break this problem into two subproblems by setting (b + 1.9375) equal to 2.872961234 and -2.872961234.Subproblem 1
b + 1.9375 = 2.872961234 Simplifying b + 1.9375 = 2.872961234 Reorder the terms: 1.9375 + b = 2.872961234 Solving 1.9375 + b = 2.872961234 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.9375' to each side of the equation. 1.9375 + -1.9375 + b = 2.872961234 + -1.9375 Combine like terms: 1.9375 + -1.9375 = 0.0000 0.0000 + b = 2.872961234 + -1.9375 b = 2.872961234 + -1.9375 Combine like terms: 2.872961234 + -1.9375 = 0.935461234 b = 0.935461234 Simplifying b = 0.935461234Subproblem 2
b + 1.9375 = -2.872961234 Simplifying b + 1.9375 = -2.872961234 Reorder the terms: 1.9375 + b = -2.872961234 Solving 1.9375 + b = -2.872961234 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.9375' to each side of the equation. 1.9375 + -1.9375 + b = -2.872961234 + -1.9375 Combine like terms: 1.9375 + -1.9375 = 0.0000 0.0000 + b = -2.872961234 + -1.9375 b = -2.872961234 + -1.9375 Combine like terms: -2.872961234 + -1.9375 = -4.810461234 b = -4.810461234 Simplifying b = -4.810461234Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.935461234, -4.810461234}Solution
b = {0, 0.935461234, -4.810461234}
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