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Simplifying 3(2b + 3) * 3(2b + 3) = 36 Reorder the terms: 3(3 + 2b) * 3(2b + 3) = 36 Reorder the terms: 3(3 + 2b) * 3(3 + 2b) = 36 Reorder the terms for easier multiplication: 3 * 3(3 + 2b)(3 + 2b) = 36 Multiply 3 * 3 9(3 + 2b)(3 + 2b) = 36 Multiply (3 + 2b) * (3 + 2b) 9(3(3 + 2b) + 2b * (3 + 2b)) = 36 9((3 * 3 + 2b * 3) + 2b * (3 + 2b)) = 36 9((9 + 6b) + 2b * (3 + 2b)) = 36 9(9 + 6b + (3 * 2b + 2b * 2b)) = 36 9(9 + 6b + (6b + 4b2)) = 36 Combine like terms: 6b + 6b = 12b 9(9 + 12b + 4b2) = 36 (9 * 9 + 12b * 9 + 4b2 * 9) = 36 (81 + 108b + 36b2) = 36 Solving 81 + 108b + 36b2 = 36 Solving for variable 'b'. Reorder the terms: 81 + -36 + 108b + 36b2 = 36 + -36 Combine like terms: 81 + -36 = 45 45 + 108b + 36b2 = 36 + -36 Combine like terms: 36 + -36 = 0 45 + 108b + 36b2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(5 + 12b + 4b2) = 0 Factor a trinomial. 9((5 + 2b)(1 + 2b)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(5 + 2b)' equal to zero and attempt to solve: Simplifying 5 + 2b = 0 Solving 5 + 2b = 0 Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2b = 0 + -5 2b = 0 + -5 Combine like terms: 0 + -5 = -5 2b = -5 Divide each side by '2'. b = -2.5 Simplifying b = -2.5Subproblem 2
Set the factor '(1 + 2b)' equal to zero and attempt to solve: Simplifying 1 + 2b = 0 Solving 1 + 2b = 0 Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2b = 0 + -1 2b = 0 + -1 Combine like terms: 0 + -1 = -1 2b = -1 Divide each side by '2'. b = -0.5 Simplifying b = -0.5Solution
b = {-2.5, -0.5}
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