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Simplifying 20b2 + -27b + 8 = 0 Reorder the terms: 8 + -27b + 20b2 = 0 Solving 8 + -27b + 20b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.4 + -1.35b + b2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -1.35b + -0.4 + b2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -1.35b + b2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -1.35b + b2 = 0 + -0.4 -1.35b + b2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -1.35b + b2 = -0.4 The b term is -1.35b. Take half its coefficient (-0.675). Square it (0.455625) and add it to both sides. Add '0.455625' to each side of the equation. -1.35b + 0.455625 + b2 = -0.4 + 0.455625 Reorder the terms: 0.455625 + -1.35b + b2 = -0.4 + 0.455625 Combine like terms: -0.4 + 0.455625 = 0.055625 0.455625 + -1.35b + b2 = 0.055625 Factor a perfect square on the left side: (b + -0.675)(b + -0.675) = 0.055625 Calculate the square root of the right side: 0.235849528 Break this problem into two subproblems by setting (b + -0.675) equal to 0.235849528 and -0.235849528.Subproblem 1
b + -0.675 = 0.235849528 Simplifying b + -0.675 = 0.235849528 Reorder the terms: -0.675 + b = 0.235849528 Solving -0.675 + b = 0.235849528 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.675' to each side of the equation. -0.675 + 0.675 + b = 0.235849528 + 0.675 Combine like terms: -0.675 + 0.675 = 0.000 0.000 + b = 0.235849528 + 0.675 b = 0.235849528 + 0.675 Combine like terms: 0.235849528 + 0.675 = 0.910849528 b = 0.910849528 Simplifying b = 0.910849528Subproblem 2
b + -0.675 = -0.235849528 Simplifying b + -0.675 = -0.235849528 Reorder the terms: -0.675 + b = -0.235849528 Solving -0.675 + b = -0.235849528 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.675' to each side of the equation. -0.675 + 0.675 + b = -0.235849528 + 0.675 Combine like terms: -0.675 + 0.675 = 0.000 0.000 + b = -0.235849528 + 0.675 b = -0.235849528 + 0.675 Combine like terms: -0.235849528 + 0.675 = 0.439150472 b = 0.439150472 Simplifying b = 0.439150472Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.910849528, 0.439150472}
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