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Simplifying 9(6b + 5) + -4b(b + 3) = 0 Reorder the terms: 9(5 + 6b) + -4b(b + 3) = 0 (5 * 9 + 6b * 9) + -4b(b + 3) = 0 (45 + 54b) + -4b(b + 3) = 0 Reorder the terms: 45 + 54b + -4b(3 + b) = 0 45 + 54b + (3 * -4b + b * -4b) = 0 45 + 54b + (-12b + -4b2) = 0 Combine like terms: 54b + -12b = 42b 45 + 42b + -4b2 = 0 Solving 45 + 42b + -4b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -11.25 + -10.5b + b2 = 0 Move the constant term to the right: Add '11.25' to each side of the equation. -11.25 + -10.5b + 11.25 + b2 = 0 + 11.25 Reorder the terms: -11.25 + 11.25 + -10.5b + b2 = 0 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + -10.5b + b2 = 0 + 11.25 -10.5b + b2 = 0 + 11.25 Combine like terms: 0 + 11.25 = 11.25 -10.5b + b2 = 11.25 The b term is -10.5b. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5b + 27.5625 + b2 = 11.25 + 27.5625 Reorder the terms: 27.5625 + -10.5b + b2 = 11.25 + 27.5625 Combine like terms: 11.25 + 27.5625 = 38.8125 27.5625 + -10.5b + b2 = 38.8125 Factor a perfect square on the left side: (b + -5.25)(b + -5.25) = 38.8125 Calculate the square root of the right side: 6.229967897 Break this problem into two subproblems by setting (b + -5.25) equal to 6.229967897 and -6.229967897.Subproblem 1
b + -5.25 = 6.229967897 Simplifying b + -5.25 = 6.229967897 Reorder the terms: -5.25 + b = 6.229967897 Solving -5.25 + b = 6.229967897 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + b = 6.229967897 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + b = 6.229967897 + 5.25 b = 6.229967897 + 5.25 Combine like terms: 6.229967897 + 5.25 = 11.479967897 b = 11.479967897 Simplifying b = 11.479967897Subproblem 2
b + -5.25 = -6.229967897 Simplifying b + -5.25 = -6.229967897 Reorder the terms: -5.25 + b = -6.229967897 Solving -5.25 + b = -6.229967897 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + b = -6.229967897 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + b = -6.229967897 + 5.25 b = -6.229967897 + 5.25 Combine like terms: -6.229967897 + 5.25 = -0.979967897 b = -0.979967897 Simplifying b = -0.979967897Solution
The solution to the problem is based on the solutions from the subproblems. b = {11.479967897, -0.979967897}
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