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Simplifying b2 + 24b = 16 Reorder the terms: 24b + b2 = 16 Solving 24b + b2 = 16 Solving for variable 'b'. Reorder the terms: -16 + 24b + b2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + 24b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 24b + 16 + b2 = 0 + 16 Reorder the terms: -16 + 16 + 24b + b2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 24b + b2 = 0 + 16 24b + b2 = 0 + 16 Combine like terms: 0 + 16 = 16 24b + b2 = 16 The b term is 24b. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24b + 144 + b2 = 16 + 144 Reorder the terms: 144 + 24b + b2 = 16 + 144 Combine like terms: 16 + 144 = 160 144 + 24b + b2 = 160 Factor a perfect square on the left side: (b + 12)(b + 12) = 160 Calculate the square root of the right side: 12.649110641 Break this problem into two subproblems by setting (b + 12) equal to 12.649110641 and -12.649110641.Subproblem 1
b + 12 = 12.649110641 Simplifying b + 12 = 12.649110641 Reorder the terms: 12 + b = 12.649110641 Solving 12 + b = 12.649110641 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + b = 12.649110641 + -12 Combine like terms: 12 + -12 = 0 0 + b = 12.649110641 + -12 b = 12.649110641 + -12 Combine like terms: 12.649110641 + -12 = 0.649110641 b = 0.649110641 Simplifying b = 0.649110641Subproblem 2
b + 12 = -12.649110641 Simplifying b + 12 = -12.649110641 Reorder the terms: 12 + b = -12.649110641 Solving 12 + b = -12.649110641 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + b = -12.649110641 + -12 Combine like terms: 12 + -12 = 0 0 + b = -12.649110641 + -12 b = -12.649110641 + -12 Combine like terms: -12.649110641 + -12 = -24.649110641 b = -24.649110641 Simplifying b = -24.649110641Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.649110641, -24.649110641}
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