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Simplifying 0.5b2 + 3b + -36 = 0 Reorder the terms: -36 + 3b + 0.5b2 = 0 Solving -36 + 3b + 0.5b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -72 + 6b + b2 = 0 Move the constant term to the right: Add '72' to each side of the equation. -72 + 6b + 72 + b2 = 0 + 72 Reorder the terms: -72 + 72 + 6b + b2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 6b + b2 = 0 + 72 6b + b2 = 0 + 72 Combine like terms: 0 + 72 = 72 6b + b2 = 72 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 = 72 + 9 Reorder the terms: 9 + 6b + b2 = 72 + 9 Combine like terms: 72 + 9 = 81 9 + 6b + b2 = 81 Factor a perfect square on the left side: (b + 3)(b + 3) = 81 Calculate the square root of the right side: 9 Break this problem into two subproblems by setting (b + 3) equal to 9 and -9.Subproblem 1
b + 3 = 9 Simplifying b + 3 = 9 Reorder the terms: 3 + b = 9 Solving 3 + b = 9 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 = 9 + -3 Combine like terms: 3 + -3 = 0 0 + b = 9 + -3 b = 9 + -3 Combine like terms: 9 + -3 = 6 b = 6 Simplifying b = 6Subproblem 2
b + 3 = -9 Simplifying b + 3 = -9 Reorder the terms: 3 + b = -9 Solving 3 + b = -9 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 = -9 + -3 Combine like terms: 3 + -3 = 0 0 + b = -9 + -3 b = -9 + -3 Combine like terms: -9 + -3 = -12 b = -12 Simplifying b = -12Solution
The solution to the problem is based on the solutions from the subproblems. b = {6, -12}
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