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Simplifying 16b2 + -48b + 30 = 0 Reorder the terms: 30 + -48b + 16b2 = 0 Solving 30 + -48b + 16b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -24b + 8b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + -24b + 8b2)' equal to zero and attempt to solve: Simplifying 15 + -24b + 8b2 = 0 Solving 15 + -24b + 8b2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.875 + -3b + b2 = 0 Move the constant term to the right: Add '-1.875' to each side of the equation. 1.875 + -3b + -1.875 + b2 = 0 + -1.875 Reorder the terms: 1.875 + -1.875 + -3b + b2 = 0 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + -3b + b2 = 0 + -1.875 -3b + b2 = 0 + -1.875 Combine like terms: 0 + -1.875 = -1.875 -3b + b2 = -1.875 The b term is -3b. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3b + 2.25 + b2 = -1.875 + 2.25 Reorder the terms: 2.25 + -3b + b2 = -1.875 + 2.25 Combine like terms: -1.875 + 2.25 = 0.375 2.25 + -3b + b2 = 0.375 Factor a perfect square on the left side: (b + -1.5)(b + -1.5) = 0.375 Calculate the square root of the right side: 0.612372436 Break this problem into two subproblems by setting (b + -1.5) equal to 0.612372436 and -0.612372436.Subproblem 1
b + -1.5 = 0.612372436 Simplifying b + -1.5 = 0.612372436 Reorder the terms: -1.5 + b = 0.612372436 Solving -1.5 + b = 0.612372436 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + b = 0.612372436 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + b = 0.612372436 + 1.5 b = 0.612372436 + 1.5 Combine like terms: 0.612372436 + 1.5 = 2.112372436 b = 2.112372436 Simplifying b = 2.112372436Subproblem 2
b + -1.5 = -0.612372436 Simplifying b + -1.5 = -0.612372436 Reorder the terms: -1.5 + b = -0.612372436 Solving -1.5 + b = -0.612372436 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + b = -0.612372436 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + b = -0.612372436 + 1.5 b = -0.612372436 + 1.5 Combine like terms: -0.612372436 + 1.5 = 0.887627564 b = 0.887627564 Simplifying b = 0.887627564Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.112372436, 0.887627564}Solution
b = {2.112372436, 0.887627564}
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