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Simplifying 10b2 + 8b = 16 Reorder the terms: 8b + 10b2 = 16 Solving 8b + 10b2 = 16 Solving for variable 'b'. Reorder the terms: -16 + 8b + 10b2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + 8b + 10b2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 4b + 5b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 4b + 5b2)' equal to zero and attempt to solve: Simplifying -8 + 4b + 5b2 = 0 Solving -8 + 4b + 5b2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + 0.8b + b2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + 0.8b + 1.6 + b2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + 0.8b + b2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + 0.8b + b2 = 0 + 1.6 0.8b + b2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 0.8b + b2 = 1.6 The b term is 0.8b. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8b + 0.16 + b2 = 1.6 + 0.16 Reorder the terms: 0.16 + 0.8b + b2 = 1.6 + 0.16 Combine like terms: 1.6 + 0.16 = 1.76 0.16 + 0.8b + b2 = 1.76 Factor a perfect square on the left side: (b + 0.4)(b + 0.4) = 1.76 Calculate the square root of the right side: 1.326649916 Break this problem into two subproblems by setting (b + 0.4) equal to 1.326649916 and -1.326649916.Subproblem 1
b + 0.4 = 1.326649916 Simplifying b + 0.4 = 1.326649916 Reorder the terms: 0.4 + b = 1.326649916 Solving 0.4 + b = 1.326649916 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + b = 1.326649916 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + b = 1.326649916 + -0.4 b = 1.326649916 + -0.4 Combine like terms: 1.326649916 + -0.4 = 0.926649916 b = 0.926649916 Simplifying b = 0.926649916Subproblem 2
b + 0.4 = -1.326649916 Simplifying b + 0.4 = -1.326649916 Reorder the terms: 0.4 + b = -1.326649916 Solving 0.4 + b = -1.326649916 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + b = -1.326649916 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + b = -1.326649916 + -0.4 b = -1.326649916 + -0.4 Combine like terms: -1.326649916 + -0.4 = -1.726649916 b = -1.726649916 Simplifying b = -1.726649916Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.926649916, -1.726649916}Solution
b = {0.926649916, -1.726649916}
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