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Simplifying 12b2 + -72b + 27 = 0 Reorder the terms: 27 + -72b + 12b2 = 0 Solving 27 + -72b + 12b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '3'. 3(9 + -24b + 4b2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(9 + -24b + 4b2)' equal to zero and attempt to solve: Simplifying 9 + -24b + 4b2 = 0 Solving 9 + -24b + 4b2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + -6b + b2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -6b + -2.25 + b2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -6b + b2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -6b + b2 = 0 + -2.25 -6b + b2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -6b + b2 = -2.25 The b term is -6b. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6b + 9 + b2 = -2.25 + 9 Reorder the terms: 9 + -6b + b2 = -2.25 + 9 Combine like terms: -2.25 + 9 = 6.75 9 + -6b + b2 = 6.75 Factor a perfect square on the left side: (b + -3)(b + -3) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (b + -3) equal to 2.598076211 and -2.598076211.Subproblem 1
b + -3 = 2.598076211 Simplifying b + -3 = 2.598076211 Reorder the terms: -3 + b = 2.598076211 Solving -3 + b = 2.598076211 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + b = 2.598076211 + 3 Combine like terms: -3 + 3 = 0 0 + b = 2.598076211 + 3 b = 2.598076211 + 3 Combine like terms: 2.598076211 + 3 = 5.598076211 b = 5.598076211 Simplifying b = 5.598076211Subproblem 2
b + -3 = -2.598076211 Simplifying b + -3 = -2.598076211 Reorder the terms: -3 + b = -2.598076211 Solving -3 + b = -2.598076211 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + b = -2.598076211 + 3 Combine like terms: -3 + 3 = 0 0 + b = -2.598076211 + 3 b = -2.598076211 + 3 Combine like terms: -2.598076211 + 3 = 0.401923789 b = 0.401923789 Simplifying b = 0.401923789Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.598076211, 0.401923789}Solution
b = {5.598076211, 0.401923789}
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