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Simplifying -7b + 3(4b + 8) * b = 4 Reorder the terms: -7b + 3(8 + 4b) * b = 4 Reorder the terms for easier multiplication: -7b + 3b(8 + 4b) = 4 -7b + (8 * 3b + 4b * 3b) = 4 -7b + (24b + 12b2) = 4 Combine like terms: -7b + 24b = 17b 17b + 12b2 = 4 Solving 17b + 12b2 = 4 Solving for variable 'b'. Reorder the terms: -4 + 17b + 12b2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 17b + 12b2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.3333333333 + 1.416666667b + b2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 1.416666667b + 0.3333333333 + b2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 1.416666667b + b2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 1.416666667b + b2 = 0 + 0.3333333333 1.416666667b + b2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 1.416666667b + b2 = 0.3333333333 The b term is 1.416666667b. Take half its coefficient (0.7083333335). Square it (0.5017361113) and add it to both sides. Add '0.5017361113' to each side of the equation. 1.416666667b + 0.5017361113 + b2 = 0.3333333333 + 0.5017361113 Reorder the terms: 0.5017361113 + 1.416666667b + b2 = 0.3333333333 + 0.5017361113 Combine like terms: 0.3333333333 + 0.5017361113 = 0.8350694446 0.5017361113 + 1.416666667b + b2 = 0.8350694446 Factor a perfect square on the left side: (b + 0.7083333335)(b + 0.7083333335) = 0.8350694446 Calculate the square root of the right side: 0.913821342 Break this problem into two subproblems by setting (b + 0.7083333335) equal to 0.913821342 and -0.913821342.Subproblem 1
b + 0.7083333335 = 0.913821342 Simplifying b + 0.7083333335 = 0.913821342 Reorder the terms: 0.7083333335 + b = 0.913821342 Solving 0.7083333335 + b = 0.913821342 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.7083333335' to each side of the equation. 0.7083333335 + -0.7083333335 + b = 0.913821342 + -0.7083333335 Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000 0.0000000000 + b = 0.913821342 + -0.7083333335 b = 0.913821342 + -0.7083333335 Combine like terms: 0.913821342 + -0.7083333335 = 0.2054880085 b = 0.2054880085 Simplifying b = 0.2054880085Subproblem 2
b + 0.7083333335 = -0.913821342 Simplifying b + 0.7083333335 = -0.913821342 Reorder the terms: 0.7083333335 + b = -0.913821342 Solving 0.7083333335 + b = -0.913821342 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.7083333335' to each side of the equation. 0.7083333335 + -0.7083333335 + b = -0.913821342 + -0.7083333335 Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000 0.0000000000 + b = -0.913821342 + -0.7083333335 b = -0.913821342 + -0.7083333335 Combine like terms: -0.913821342 + -0.7083333335 = -1.6221546755 b = -1.6221546755 Simplifying b = -1.6221546755Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.2054880085, -1.6221546755}
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