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Simplifying (4b * 4b) + -8b + -5 = 0 Reorder the terms for easier multiplication: (4 * 4b * b) + -8b + -5 = 0 Multiply 4 * 4 (16b * b) + -8b + -5 = 0 Multiply b * b (16b2) + -8b + -5 = 0 Reorder the terms: -5 + -8b + (16b2) = 0 Solving -5 + -8b + (16b2) = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.3125 + -0.5b + b2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -0.5b + 0.3125 + b2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -0.5b + b2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -0.5b + b2 = 0 + 0.3125 -0.5b + b2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -0.5b + b2 = 0.3125 The b term is -0.5b. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5b + 0.0625 + b2 = 0.3125 + 0.0625 Reorder the terms: 0.0625 + -0.5b + b2 = 0.3125 + 0.0625 Combine like terms: 0.3125 + 0.0625 = 0.375 0.0625 + -0.5b + b2 = 0.375 Factor a perfect square on the left side: ((b) + -0.25)((b) + -0.25) = 0.375 Calculate the square root of the right side: 0.612372436 Break this problem into two subproblems by setting ((b) + -0.25) equal to 0.612372436 and -0.612372436.Subproblem 1
(b) + -0.25 = 0.612372436 Simplifying (b) + -0.25 = 0.612372436 b + -0.25 = 0.612372436 Reorder the terms: -0.25 + b = 0.612372436 Solving -0.25 + b = 0.612372436 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + b = 0.612372436 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + b = 0.612372436 + 0.25 b = 0.612372436 + 0.25 Combine like terms: 0.612372436 + 0.25 = 0.862372436 b = 0.862372436 Simplifying b = 0.862372436Subproblem 2
(b) + -0.25 = -0.612372436 Simplifying (b) + -0.25 = -0.612372436 b + -0.25 = -0.612372436 Reorder the terms: -0.25 + b = -0.612372436 Solving -0.25 + b = -0.612372436 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + b = -0.612372436 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + b = -0.612372436 + 0.25 b = -0.612372436 + 0.25 Combine like terms: -0.612372436 + 0.25 = -0.362372436 b = -0.362372436 Simplifying b = -0.362372436Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.862372436, -0.362372436}
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