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Simplifying 10b4 + 32b3 + -18b2 = 0 Reorder the terms: -18b2 + 32b3 + 10b4 = 0 Solving -18b2 + 32b3 + 10b4 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2b2'. 2b2(-9 + 16b + 5b2) = 0 Ignore the factor 2.Subproblem 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 '(-9 + 16b + 5b2)' equal to zero and attempt to solve: Simplifying -9 + 16b + 5b2 = 0 Solving -9 + 16b + 5b2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + 3.2b + b2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 3.2b + 1.8 + b2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 3.2b + b2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 3.2b + b2 = 0 + 1.8 3.2b + b2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 3.2b + b2 = 1.8 The b term is 3.2b. Take half its coefficient (1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. 3.2b + 2.56 + b2 = 1.8 + 2.56 Reorder the terms: 2.56 + 3.2b + b2 = 1.8 + 2.56 Combine like terms: 1.8 + 2.56 = 4.36 2.56 + 3.2b + b2 = 4.36 Factor a perfect square on the left side: (b + 1.6)(b + 1.6) = 4.36 Calculate the square root of the right side: 2.088061302 Break this problem into two subproblems by setting (b + 1.6) equal to 2.088061302 and -2.088061302.Subproblem 1
b + 1.6 = 2.088061302 Simplifying b + 1.6 = 2.088061302 Reorder the terms: 1.6 + b = 2.088061302 Solving 1.6 + b = 2.088061302 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + b = 2.088061302 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + b = 2.088061302 + -1.6 b = 2.088061302 + -1.6 Combine like terms: 2.088061302 + -1.6 = 0.488061302 b = 0.488061302 Simplifying b = 0.488061302Subproblem 2
b + 1.6 = -2.088061302 Simplifying b + 1.6 = -2.088061302 Reorder the terms: 1.6 + b = -2.088061302 Solving 1.6 + b = -2.088061302 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + b = -2.088061302 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + b = -2.088061302 + -1.6 b = -2.088061302 + -1.6 Combine like terms: -2.088061302 + -1.6 = -3.688061302 b = -3.688061302 Simplifying b = -3.688061302Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.488061302, -3.688061302}Solution
b = {0, 0.488061302, -3.688061302}
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