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Simplifying b(b + 6) = 36 Reorder the terms: b(6 + b) = 36 (6 * b + b * b) = 36 (6b + b2) = 36 Solving 6b + b2 = 36 Solving for variable 'b'. Reorder the terms: -36 + 6b + b2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + 6b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 6b + 36 + b2 = 0 + 36 Reorder the terms: -36 + 36 + 6b + b2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 6b + b2 = 0 + 36 6b + b2 = 0 + 36 Combine like terms: 0 + 36 = 36 6b + b2 = 36 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 = 36 + 9 Reorder the terms: 9 + 6b + b2 = 36 + 9 Combine like terms: 36 + 9 = 45 9 + 6b + b2 = 45 Factor a perfect square on the left side: (b + 3)(b + 3) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (b + 3) equal to 6.708203933 and -6.708203933.Subproblem 1
b + 3 = 6.708203933 Simplifying b + 3 = 6.708203933 Reorder the terms: 3 + b = 6.708203933 Solving 3 + b = 6.708203933 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 = 6.708203933 + -3 Combine like terms: 3 + -3 = 0 0 + b = 6.708203933 + -3 b = 6.708203933 + -3 Combine like terms: 6.708203933 + -3 = 3.708203933 b = 3.708203933 Simplifying b = 3.708203933Subproblem 2
b + 3 = -6.708203933 Simplifying b + 3 = -6.708203933 Reorder the terms: 3 + b = -6.708203933 Solving 3 + b = -6.708203933 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 = -6.708203933 + -3 Combine like terms: 3 + -3 = 0 0 + b = -6.708203933 + -3 b = -6.708203933 + -3 Combine like terms: -6.708203933 + -3 = -9.708203933 b = -9.708203933 Simplifying b = -9.708203933Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.708203933, -9.708203933}
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