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Simplifying 10b2 + -15 = 8b + -12 Reorder the terms: -15 + 10b2 = 8b + -12 Reorder the terms: -15 + 10b2 = -12 + 8b Solving -15 + 10b2 = -12 + 8b Solving for variable 'b'. Reorder the terms: -15 + 12 + -8b + 10b2 = -12 + 8b + 12 + -8b Combine like terms: -15 + 12 = -3 -3 + -8b + 10b2 = -12 + 8b + 12 + -8b Reorder the terms: -3 + -8b + 10b2 = -12 + 12 + 8b + -8b Combine like terms: -12 + 12 = 0 -3 + -8b + 10b2 = 0 + 8b + -8b -3 + -8b + 10b2 = 8b + -8b Combine like terms: 8b + -8b = 0 -3 + -8b + 10b2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.3 + -0.8b + b2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + -0.8b + 0.3 + b2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + -0.8b + b2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + -0.8b + b2 = 0 + 0.3 -0.8b + b2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 -0.8b + b2 = 0.3 The b term is -0.8b. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8b + 0.16 + b2 = 0.3 + 0.16 Reorder the terms: 0.16 + -0.8b + b2 = 0.3 + 0.16 Combine like terms: 0.3 + 0.16 = 0.46 0.16 + -0.8b + b2 = 0.46 Factor a perfect square on the left side: (b + -0.4)(b + -0.4) = 0.46 Calculate the square root of the right side: 0.678232998 Break this problem into two subproblems by setting (b + -0.4) equal to 0.678232998 and -0.678232998.Subproblem 1
b + -0.4 = 0.678232998 Simplifying b + -0.4 = 0.678232998 Reorder the terms: -0.4 + b = 0.678232998 Solving -0.4 + b = 0.678232998 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + b = 0.678232998 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + b = 0.678232998 + 0.4 b = 0.678232998 + 0.4 Combine like terms: 0.678232998 + 0.4 = 1.078232998 b = 1.078232998 Simplifying b = 1.078232998Subproblem 2
b + -0.4 = -0.678232998 Simplifying b + -0.4 = -0.678232998 Reorder the terms: -0.4 + b = -0.678232998 Solving -0.4 + b = -0.678232998 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + b = -0.678232998 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + b = -0.678232998 + 0.4 b = -0.678232998 + 0.4 Combine like terms: -0.678232998 + 0.4 = -0.278232998 b = -0.278232998 Simplifying b = -0.278232998Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.078232998, -0.278232998}
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