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Simplifying 8b2 + -21b + 12 = 0 Reorder the terms: 12 + -21b + 8b2 = 0 Solving 12 + -21b + 8b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.5 + -2.625b + b2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -2.625b + -1.5 + b2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -2.625b + b2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -2.625b + b2 = 0 + -1.5 -2.625b + b2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -2.625b + b2 = -1.5 The b term is -2.625b. Take half its coefficient (-1.3125). Square it (1.72265625) and add it to both sides. Add '1.72265625' to each side of the equation. -2.625b + 1.72265625 + b2 = -1.5 + 1.72265625 Reorder the terms: 1.72265625 + -2.625b + b2 = -1.5 + 1.72265625 Combine like terms: -1.5 + 1.72265625 = 0.22265625 1.72265625 + -2.625b + b2 = 0.22265625 Factor a perfect square on the left side: (b + -1.3125)(b + -1.3125) = 0.22265625 Calculate the square root of the right side: 0.471864652 Break this problem into two subproblems by setting (b + -1.3125) equal to 0.471864652 and -0.471864652.Subproblem 1
b + -1.3125 = 0.471864652 Simplifying b + -1.3125 = 0.471864652 Reorder the terms: -1.3125 + b = 0.471864652 Solving -1.3125 + b = 0.471864652 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.3125' to each side of the equation. -1.3125 + 1.3125 + b = 0.471864652 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + b = 0.471864652 + 1.3125 b = 0.471864652 + 1.3125 Combine like terms: 0.471864652 + 1.3125 = 1.784364652 b = 1.784364652 Simplifying b = 1.784364652Subproblem 2
b + -1.3125 = -0.471864652 Simplifying b + -1.3125 = -0.471864652 Reorder the terms: -1.3125 + b = -0.471864652 Solving -1.3125 + b = -0.471864652 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.3125' to each side of the equation. -1.3125 + 1.3125 + b = -0.471864652 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + b = -0.471864652 + 1.3125 b = -0.471864652 + 1.3125 Combine like terms: -0.471864652 + 1.3125 = 0.840635348 b = 0.840635348 Simplifying b = 0.840635348Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.784364652, 0.840635348}
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