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Simplifying 4b2 + -17 = 12b Reorder the terms: -17 + 4b2 = 12b Solving -17 + 4b2 = 12b Solving for variable 'b'. Reorder the terms: -17 + -12b + 4b2 = 12b + -12b Combine like terms: 12b + -12b = 0 -17 + -12b + 4b2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.25 + -3b + b2 = 0 Move the constant term to the right: Add '4.25' to each side of the equation. -4.25 + -3b + 4.25 + b2 = 0 + 4.25 Reorder the terms: -4.25 + 4.25 + -3b + b2 = 0 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + -3b + b2 = 0 + 4.25 -3b + b2 = 0 + 4.25 Combine like terms: 0 + 4.25 = 4.25 -3b + b2 = 4.25 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 = 4.25 + 2.25 Reorder the terms: 2.25 + -3b + b2 = 4.25 + 2.25 Combine like terms: 4.25 + 2.25 = 6.5 2.25 + -3b + b2 = 6.5 Factor a perfect square on the left side: (b + -1.5)(b + -1.5) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (b + -1.5) equal to 2.549509757 and -2.549509757.Subproblem 1
b + -1.5 = 2.549509757 Simplifying b + -1.5 = 2.549509757 Reorder the terms: -1.5 + b = 2.549509757 Solving -1.5 + b = 2.549509757 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 = 2.549509757 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + b = 2.549509757 + 1.5 b = 2.549509757 + 1.5 Combine like terms: 2.549509757 + 1.5 = 4.049509757 b = 4.049509757 Simplifying b = 4.049509757Subproblem 2
b + -1.5 = -2.549509757 Simplifying b + -1.5 = -2.549509757 Reorder the terms: -1.5 + b = -2.549509757 Solving -1.5 + b = -2.549509757 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 = -2.549509757 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + b = -2.549509757 + 1.5 b = -2.549509757 + 1.5 Combine like terms: -2.549509757 + 1.5 = -1.049509757 b = -1.049509757 Simplifying b = -1.049509757Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.049509757, -1.049509757}
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