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Simplifying 3(b + 2) + -4b(5 + -1b) = 0 Reorder the terms: 3(2 + b) + -4b(5 + -1b) = 0 (2 * 3 + b * 3) + -4b(5 + -1b) = 0 (6 + 3b) + -4b(5 + -1b) = 0 6 + 3b + (5 * -4b + -1b * -4b) = 0 6 + 3b + (-20b + 4b2) = 0 Combine like terms: 3b + -20b = -17b 6 + -17b + 4b2 = 0 Solving 6 + -17b + 4b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.5 + -4.25b + b2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -4.25b + -1.5 + b2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -4.25b + b2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -4.25b + b2 = 0 + -1.5 -4.25b + b2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -4.25b + b2 = -1.5 The b term is -4.25b. Take half its coefficient (-2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. -4.25b + 4.515625 + b2 = -1.5 + 4.515625 Reorder the terms: 4.515625 + -4.25b + b2 = -1.5 + 4.515625 Combine like terms: -1.5 + 4.515625 = 3.015625 4.515625 + -4.25b + b2 = 3.015625 Factor a perfect square on the left side: (b + -2.125)(b + -2.125) = 3.015625 Calculate the square root of the right side: 1.736555499 Break this problem into two subproblems by setting (b + -2.125) equal to 1.736555499 and -1.736555499.Subproblem 1
b + -2.125 = 1.736555499 Simplifying b + -2.125 = 1.736555499 Reorder the terms: -2.125 + b = 1.736555499 Solving -2.125 + b = 1.736555499 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + b = 1.736555499 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + b = 1.736555499 + 2.125 b = 1.736555499 + 2.125 Combine like terms: 1.736555499 + 2.125 = 3.861555499 b = 3.861555499 Simplifying b = 3.861555499Subproblem 2
b + -2.125 = -1.736555499 Simplifying b + -2.125 = -1.736555499 Reorder the terms: -2.125 + b = -1.736555499 Solving -2.125 + b = -1.736555499 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + b = -1.736555499 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + b = -1.736555499 + 2.125 b = -1.736555499 + 2.125 Combine like terms: -1.736555499 + 2.125 = 0.388444501 b = 0.388444501 Simplifying b = 0.388444501Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.861555499, 0.388444501}
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