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Simplifying 1 + -5b + -8b2 = 0 Solving 1 + -5b + -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'. -0.125 + 0.625b + b2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + 0.625b + 0.125 + b2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + 0.625b + b2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + 0.625b + b2 = 0 + 0.125 0.625b + b2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 0.625b + b2 = 0.125 The b term is 0.625b. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625b + 0.09765625 + b2 = 0.125 + 0.09765625 Reorder the terms: 0.09765625 + 0.625b + b2 = 0.125 + 0.09765625 Combine like terms: 0.125 + 0.09765625 = 0.22265625 0.09765625 + 0.625b + b2 = 0.22265625 Factor a perfect square on the left side: (b + 0.3125)(b + 0.3125) = 0.22265625 Calculate the square root of the right side: 0.471864652 Break this problem into two subproblems by setting (b + 0.3125) equal to 0.471864652 and -0.471864652.Subproblem 1
b + 0.3125 = 0.471864652 Simplifying b + 0.3125 = 0.471864652 Reorder the terms: 0.3125 + b = 0.471864652 Solving 0.3125 + b = 0.471864652 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + b = 0.471864652 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + b = 0.471864652 + -0.3125 b = 0.471864652 + -0.3125 Combine like terms: 0.471864652 + -0.3125 = 0.159364652 b = 0.159364652 Simplifying b = 0.159364652Subproblem 2
b + 0.3125 = -0.471864652 Simplifying b + 0.3125 = -0.471864652 Reorder the terms: 0.3125 + b = -0.471864652 Solving 0.3125 + b = -0.471864652 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + b = -0.471864652 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + b = -0.471864652 + -0.3125 b = -0.471864652 + -0.3125 Combine like terms: -0.471864652 + -0.3125 = -0.784364652 b = -0.784364652 Simplifying b = -0.784364652Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.159364652, -0.784364652}
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