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Simplifying b2 + -3b = 11664 Reorder the terms: -3b + b2 = 11664 Solving -3b + b2 = 11664 Solving for variable 'b'. Reorder the terms: -11664 + -3b + b2 = 11664 + -11664 Combine like terms: 11664 + -11664 = 0 -11664 + -3b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '11664' to each side of the equation. -11664 + -3b + 11664 + b2 = 0 + 11664 Reorder the terms: -11664 + 11664 + -3b + b2 = 0 + 11664 Combine like terms: -11664 + 11664 = 0 0 + -3b + b2 = 0 + 11664 -3b + b2 = 0 + 11664 Combine like terms: 0 + 11664 = 11664 -3b + b2 = 11664 The b term is -3b. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3b + 2.25 + b2 = 11664 + 2.25 Reorder the terms: 2.25 + -3b + b2 = 11664 + 2.25 Combine like terms: 11664 + 2.25 = 11666.25 2.25 + -3b + b2 = 11666.25 Factor a perfect square on the left side: (b + -1.5)(b + -1.5) = 11666.25 Calculate the square root of the right side: 108.010416164 Break this problem into two subproblems by setting (b + -1.5) equal to 108.010416164 and -108.010416164.Subproblem 1
b + -1.5 = 108.010416164 Simplifying b + -1.5 = 108.010416164 Reorder the terms: -1.5 + b = 108.010416164 Solving -1.5 + b = 108.010416164 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + b = 108.010416164 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + b = 108.010416164 + 1.5 b = 108.010416164 + 1.5 Combine like terms: 108.010416164 + 1.5 = 109.510416164 b = 109.510416164 Simplifying b = 109.510416164Subproblem 2
b + -1.5 = -108.010416164 Simplifying b + -1.5 = -108.010416164 Reorder the terms: -1.5 + b = -108.010416164 Solving -1.5 + b = -108.010416164 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + b = -108.010416164 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + b = -108.010416164 + 1.5 b = -108.010416164 + 1.5 Combine like terms: -108.010416164 + 1.5 = -106.510416164 b = -106.510416164 Simplifying b = -106.510416164Solution
The solution to the problem is based on the solutions from the subproblems. b = {109.510416164, -106.510416164}
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