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Simplifying 2b2 + -12b + 15 = 0 Reorder the terms: 15 + -12b + 2b2 = 0 Solving 15 + -12b + 2b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + -6b + b2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -6b + -7.5 + b2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -6b + b2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -6b + b2 = 0 + -7.5 -6b + b2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -6b + b2 = -7.5 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 = -7.5 + 9 Reorder the terms: 9 + -6b + b2 = -7.5 + 9 Combine like terms: -7.5 + 9 = 1.5 9 + -6b + b2 = 1.5 Factor a perfect square on the left side: (b + -3)(b + -3) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (b + -3) equal to 1.224744871 and -1.224744871.Subproblem 1
b + -3 = 1.224744871 Simplifying b + -3 = 1.224744871 Reorder the terms: -3 + b = 1.224744871 Solving -3 + b = 1.224744871 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 = 1.224744871 + 3 Combine like terms: -3 + 3 = 0 0 + b = 1.224744871 + 3 b = 1.224744871 + 3 Combine like terms: 1.224744871 + 3 = 4.224744871 b = 4.224744871 Simplifying b = 4.224744871Subproblem 2
b + -3 = -1.224744871 Simplifying b + -3 = -1.224744871 Reorder the terms: -3 + b = -1.224744871 Solving -3 + b = -1.224744871 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 = -1.224744871 + 3 Combine like terms: -3 + 3 = 0 0 + b = -1.224744871 + 3 b = -1.224744871 + 3 Combine like terms: -1.224744871 + 3 = 1.775255129 b = 1.775255129 Simplifying b = 1.775255129Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.224744871, 1.775255129}
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