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Simplifying 20b2 + -17b = 32 Reorder the terms: -17b + 20b2 = 32 Solving -17b + 20b2 = 32 Solving for variable 'b'. Reorder the terms: -32 + -17b + 20b2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + -17b + 20b2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -1.6 + -0.85b + b2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -0.85b + 1.6 + b2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -0.85b + b2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -0.85b + b2 = 0 + 1.6 -0.85b + b2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -0.85b + b2 = 1.6 The b term is -0.85b. Take half its coefficient (-0.425). Square it (0.180625) and add it to both sides. Add '0.180625' to each side of the equation. -0.85b + 0.180625 + b2 = 1.6 + 0.180625 Reorder the terms: 0.180625 + -0.85b + b2 = 1.6 + 0.180625 Combine like terms: 1.6 + 0.180625 = 1.780625 0.180625 + -0.85b + b2 = 1.780625 Factor a perfect square on the left side: (b + -0.425)(b + -0.425) = 1.780625 Calculate the square root of the right side: 1.334400615 Break this problem into two subproblems by setting (b + -0.425) equal to 1.334400615 and -1.334400615.Subproblem 1
b + -0.425 = 1.334400615 Simplifying b + -0.425 = 1.334400615 Reorder the terms: -0.425 + b = 1.334400615 Solving -0.425 + b = 1.334400615 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.425' to each side of the equation. -0.425 + 0.425 + b = 1.334400615 + 0.425 Combine like terms: -0.425 + 0.425 = 0.000 0.000 + b = 1.334400615 + 0.425 b = 1.334400615 + 0.425 Combine like terms: 1.334400615 + 0.425 = 1.759400615 b = 1.759400615 Simplifying b = 1.759400615Subproblem 2
b + -0.425 = -1.334400615 Simplifying b + -0.425 = -1.334400615 Reorder the terms: -0.425 + b = -1.334400615 Solving -0.425 + b = -1.334400615 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.425' to each side of the equation. -0.425 + 0.425 + b = -1.334400615 + 0.425 Combine like terms: -0.425 + 0.425 = 0.000 0.000 + b = -1.334400615 + 0.425 b = -1.334400615 + 0.425 Combine like terms: -1.334400615 + 0.425 = -0.909400615 b = -0.909400615 Simplifying b = -0.909400615Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.759400615, -0.909400615}
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