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Simplifying 5b4 + -8b3 + -1b2 = 0 Reorder the terms: -1b2 + -8b3 + 5b4 = 0 Solving -1b2 + -8b3 + 5b4 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), 'b2'. b2(-1 + -8b + 5b2) = 0Subproblem 1
Set the factor 'b2' equal to zero and attempt to solve: Simplifying b2 = 0 Solving b2 = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b2 = 0 Take the square root of each side: b = {0}Subproblem 2
Set the factor '(-1 + -8b + 5b2)' equal to zero and attempt to solve: Simplifying -1 + -8b + 5b2 = 0 Solving -1 + -8b + 5b2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -1.6b + b2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -1.6b + 0.2 + b2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -1.6b + b2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -1.6b + b2 = 0 + 0.2 -1.6b + b2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -1.6b + b2 = 0.2 The b term is -1.6b. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6b + 0.64 + b2 = 0.2 + 0.64 Reorder the terms: 0.64 + -1.6b + b2 = 0.2 + 0.64 Combine like terms: 0.2 + 0.64 = 0.84 0.64 + -1.6b + b2 = 0.84 Factor a perfect square on the left side: (b + -0.8)(b + -0.8) = 0.84 Calculate the square root of the right side: 0.916515139 Break this problem into two subproblems by setting (b + -0.8) equal to 0.916515139 and -0.916515139.Subproblem 1
b + -0.8 = 0.916515139 Simplifying b + -0.8 = 0.916515139 Reorder the terms: -0.8 + b = 0.916515139 Solving -0.8 + b = 0.916515139 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + b = 0.916515139 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + b = 0.916515139 + 0.8 b = 0.916515139 + 0.8 Combine like terms: 0.916515139 + 0.8 = 1.716515139 b = 1.716515139 Simplifying b = 1.716515139Subproblem 2
b + -0.8 = -0.916515139 Simplifying b + -0.8 = -0.916515139 Reorder the terms: -0.8 + b = -0.916515139 Solving -0.8 + b = -0.916515139 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + b = -0.916515139 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + b = -0.916515139 + 0.8 b = -0.916515139 + 0.8 Combine like terms: -0.916515139 + 0.8 = -0.116515139 b = -0.116515139 Simplifying b = -0.116515139Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.716515139, -0.116515139}Solution
b = {0, 1.716515139, -0.116515139}
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