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Simplifying b2 + -6b + -24 = 0 Reorder the terms: -24 + -6b + b2 = 0 Solving -24 + -6b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -6b + 24 + b2 = 0 + 24 Reorder the terms: -24 + 24 + -6b + b2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -6b + b2 = 0 + 24 -6b + b2 = 0 + 24 Combine like terms: 0 + 24 = 24 -6b + b2 = 24 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 = 24 + 9 Reorder the terms: 9 + -6b + b2 = 24 + 9 Combine like terms: 24 + 9 = 33 9 + -6b + b2 = 33 Factor a perfect square on the left side: (b + -3)(b + -3) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (b + -3) equal to 5.744562647 and -5.744562647.Subproblem 1
b + -3 = 5.744562647 Simplifying b + -3 = 5.744562647 Reorder the terms: -3 + b = 5.744562647 Solving -3 + b = 5.744562647 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 = 5.744562647 + 3 Combine like terms: -3 + 3 = 0 0 + b = 5.744562647 + 3 b = 5.744562647 + 3 Combine like terms: 5.744562647 + 3 = 8.744562647 b = 8.744562647 Simplifying b = 8.744562647Subproblem 2
b + -3 = -5.744562647 Simplifying b + -3 = -5.744562647 Reorder the terms: -3 + b = -5.744562647 Solving -3 + b = -5.744562647 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 = -5.744562647 + 3 Combine like terms: -3 + 3 = 0 0 + b = -5.744562647 + 3 b = -5.744562647 + 3 Combine like terms: -5.744562647 + 3 = -2.744562647 b = -2.744562647 Simplifying b = -2.744562647Solution
The solution to the problem is based on the solutions from the subproblems. b = {8.744562647, -2.744562647}
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