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Simplifying -2(b + -6) * 4b = 2b + 7 Reorder the terms: -2(-6 + b) * 4b = 2b + 7 Reorder the terms for easier multiplication: -2 * 4b(-6 + b) = 2b + 7 Multiply -2 * 4 -8b(-6 + b) = 2b + 7 (-6 * -8b + b * -8b) = 2b + 7 (48b + -8b2) = 2b + 7 Reorder the terms: 48b + -8b2 = 7 + 2b Solving 48b + -8b2 = 7 + 2b Solving for variable 'b'. Reorder the terms: -7 + 48b + -2b + -8b2 = 7 + 2b + -7 + -2b Combine like terms: 48b + -2b = 46b -7 + 46b + -8b2 = 7 + 2b + -7 + -2b Reorder the terms: -7 + 46b + -8b2 = 7 + -7 + 2b + -2b Combine like terms: 7 + -7 = 0 -7 + 46b + -8b2 = 0 + 2b + -2b -7 + 46b + -8b2 = 2b + -2b Combine like terms: 2b + -2b = 0 -7 + 46b + -8b2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 0.875 + -5.75b + b2 = 0 Move the constant term to the right: Add '-0.875' to each side of the equation. 0.875 + -5.75b + -0.875 + b2 = 0 + -0.875 Reorder the terms: 0.875 + -0.875 + -5.75b + b2 = 0 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + -5.75b + b2 = 0 + -0.875 -5.75b + b2 = 0 + -0.875 Combine like terms: 0 + -0.875 = -0.875 -5.75b + b2 = -0.875 The b term is -5.75b. Take half its coefficient (-2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. -5.75b + 8.265625 + b2 = -0.875 + 8.265625 Reorder the terms: 8.265625 + -5.75b + b2 = -0.875 + 8.265625 Combine like terms: -0.875 + 8.265625 = 7.390625 8.265625 + -5.75b + b2 = 7.390625 Factor a perfect square on the left side: (b + -2.875)(b + -2.875) = 7.390625 Calculate the square root of the right side: 2.718570396 Break this problem into two subproblems by setting (b + -2.875) equal to 2.718570396 and -2.718570396.Subproblem 1
b + -2.875 = 2.718570396 Simplifying b + -2.875 = 2.718570396 Reorder the terms: -2.875 + b = 2.718570396 Solving -2.875 + b = 2.718570396 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + b = 2.718570396 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + b = 2.718570396 + 2.875 b = 2.718570396 + 2.875 Combine like terms: 2.718570396 + 2.875 = 5.593570396 b = 5.593570396 Simplifying b = 5.593570396Subproblem 2
b + -2.875 = -2.718570396 Simplifying b + -2.875 = -2.718570396 Reorder the terms: -2.875 + b = -2.718570396 Solving -2.875 + b = -2.718570396 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + b = -2.718570396 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + b = -2.718570396 + 2.875 b = -2.718570396 + 2.875 Combine like terms: -2.718570396 + 2.875 = 0.156429604 b = 0.156429604 Simplifying b = 0.156429604Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.593570396, 0.156429604}
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