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Simplifying 20b2 + -15 = 8b + -12 Reorder the terms: -15 + 20b2 = 8b + -12 Reorder the terms: -15 + 20b2 = -12 + 8b Solving -15 + 20b2 = -12 + 8b Solving for variable 'b'. Reorder the terms: -15 + 12 + -8b + 20b2 = -12 + 8b + 12 + -8b Combine like terms: -15 + 12 = -3 -3 + -8b + 20b2 = -12 + 8b + 12 + -8b Reorder the terms: -3 + -8b + 20b2 = -12 + 12 + 8b + -8b Combine like terms: -12 + 12 = 0 -3 + -8b + 20b2 = 0 + 8b + -8b -3 + -8b + 20b2 = 8b + -8b Combine like terms: 8b + -8b = 0 -3 + -8b + 20b2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.15 + -0.4b + b2 = 0 Move the constant term to the right: Add '0.15' to each side of the equation. -0.15 + -0.4b + 0.15 + b2 = 0 + 0.15 Reorder the terms: -0.15 + 0.15 + -0.4b + b2 = 0 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + -0.4b + b2 = 0 + 0.15 -0.4b + b2 = 0 + 0.15 Combine like terms: 0 + 0.15 = 0.15 -0.4b + b2 = 0.15 The b term is -0.4b. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4b + 0.04 + b2 = 0.15 + 0.04 Reorder the terms: 0.04 + -0.4b + b2 = 0.15 + 0.04 Combine like terms: 0.15 + 0.04 = 0.19 0.04 + -0.4b + b2 = 0.19 Factor a perfect square on the left side: (b + -0.2)(b + -0.2) = 0.19 Calculate the square root of the right side: 0.435889894 Break this problem into two subproblems by setting (b + -0.2) equal to 0.435889894 and -0.435889894.Subproblem 1
b + -0.2 = 0.435889894 Simplifying b + -0.2 = 0.435889894 Reorder the terms: -0.2 + b = 0.435889894 Solving -0.2 + b = 0.435889894 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + b = 0.435889894 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + b = 0.435889894 + 0.2 b = 0.435889894 + 0.2 Combine like terms: 0.435889894 + 0.2 = 0.635889894 b = 0.635889894 Simplifying b = 0.635889894Subproblem 2
b + -0.2 = -0.435889894 Simplifying b + -0.2 = -0.435889894 Reorder the terms: -0.2 + b = -0.435889894 Solving -0.2 + b = -0.435889894 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + b = -0.435889894 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + b = -0.435889894 + 0.2 b = -0.435889894 + 0.2 Combine like terms: -0.435889894 + 0.2 = -0.235889894 b = -0.235889894 Simplifying b = -0.235889894Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.635889894, -0.235889894}
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