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Simplifying 1.50b2 + -24b + -24 = 0 Reorder the terms: -24 + -24b + 1.50b2 = 0 Solving -24 + -24b + 1.50b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 1.50 the coefficient of the squared term: Divide each side by '1.50'. -16 + -16b + b2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -16b + 16 + b2 = 0 + 16 Reorder the terms: -16 + 16 + -16b + b2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -16b + b2 = 0 + 16 -16b + b2 = 0 + 16 Combine like terms: 0 + 16 = 16 -16b + b2 = 16 The b term is -16b. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16b + 64 + b2 = 16 + 64 Reorder the terms: 64 + -16b + b2 = 16 + 64 Combine like terms: 16 + 64 = 80 64 + -16b + b2 = 80 Factor a perfect square on the left side: (b + -8)(b + -8) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (b + -8) equal to 8.94427191 and -8.94427191.Subproblem 1
b + -8 = 8.94427191 Simplifying b + -8 = 8.94427191 Reorder the terms: -8 + b = 8.94427191 Solving -8 + b = 8.94427191 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + b = 8.94427191 + 8 Combine like terms: -8 + 8 = 0 0 + b = 8.94427191 + 8 b = 8.94427191 + 8 Combine like terms: 8.94427191 + 8 = 16.94427191 b = 16.94427191 Simplifying b = 16.94427191Subproblem 2
b + -8 = -8.94427191 Simplifying b + -8 = -8.94427191 Reorder the terms: -8 + b = -8.94427191 Solving -8 + b = -8.94427191 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + b = -8.94427191 + 8 Combine like terms: -8 + 8 = 0 0 + b = -8.94427191 + 8 b = -8.94427191 + 8 Combine like terms: -8.94427191 + 8 = -0.94427191 b = -0.94427191 Simplifying b = -0.94427191Solution
The solution to the problem is based on the solutions from the subproblems. b = {16.94427191, -0.94427191}
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