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Simplifying 8b2 + -1b + -2 = 0 Reorder the terms: -2 + -1b + 8b2 = 0 Solving -2 + -1b + 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'. -0.25 + -0.125b + b2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -0.125b + 0.25 + b2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -0.125b + b2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.125b + b2 = 0 + 0.25 -0.125b + b2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -0.125b + b2 = 0.25 The b term is -0.125b. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125b + 0.00390625 + b2 = 0.25 + 0.00390625 Reorder the terms: 0.00390625 + -0.125b + b2 = 0.25 + 0.00390625 Combine like terms: 0.25 + 0.00390625 = 0.25390625 0.00390625 + -0.125b + b2 = 0.25390625 Factor a perfect square on the left side: (b + -0.0625)(b + -0.0625) = 0.25390625 Calculate the square root of the right side: 0.503891109 Break this problem into two subproblems by setting (b + -0.0625) equal to 0.503891109 and -0.503891109.Subproblem 1
b + -0.0625 = 0.503891109 Simplifying b + -0.0625 = 0.503891109 Reorder the terms: -0.0625 + b = 0.503891109 Solving -0.0625 + b = 0.503891109 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + b = 0.503891109 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + b = 0.503891109 + 0.0625 b = 0.503891109 + 0.0625 Combine like terms: 0.503891109 + 0.0625 = 0.566391109 b = 0.566391109 Simplifying b = 0.566391109Subproblem 2
b + -0.0625 = -0.503891109 Simplifying b + -0.0625 = -0.503891109 Reorder the terms: -0.0625 + b = -0.503891109 Solving -0.0625 + b = -0.503891109 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + b = -0.503891109 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + b = -0.503891109 + 0.0625 b = -0.503891109 + 0.0625 Combine like terms: -0.503891109 + 0.0625 = -0.441391109 b = -0.441391109 Simplifying b = -0.441391109Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.566391109, -0.441391109}
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