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Simplifying 8b2 + -5b + -10 = 0 Reorder the terms: -10 + -5b + 8b2 = 0 Solving -10 + -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'. -1.25 + -0.625b + b2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -0.625b + 1.25 + b2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -0.625b + b2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -0.625b + b2 = 0 + 1.25 -0.625b + b2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -0.625b + b2 = 1.25 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 = 1.25 + 0.09765625 Reorder the terms: 0.09765625 + -0.625b + b2 = 1.25 + 0.09765625 Combine like terms: 1.25 + 0.09765625 = 1.34765625 0.09765625 + -0.625b + b2 = 1.34765625 Factor a perfect square on the left side: (b + -0.3125)(b + -0.3125) = 1.34765625 Calculate the square root of the right side: 1.160885976 Break this problem into two subproblems by setting (b + -0.3125) equal to 1.160885976 and -1.160885976.Subproblem 1
b + -0.3125 = 1.160885976 Simplifying b + -0.3125 = 1.160885976 Reorder the terms: -0.3125 + b = 1.160885976 Solving -0.3125 + b = 1.160885976 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 = 1.160885976 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + b = 1.160885976 + 0.3125 b = 1.160885976 + 0.3125 Combine like terms: 1.160885976 + 0.3125 = 1.473385976 b = 1.473385976 Simplifying b = 1.473385976Subproblem 2
b + -0.3125 = -1.160885976 Simplifying b + -0.3125 = -1.160885976 Reorder the terms: -0.3125 + b = -1.160885976 Solving -0.3125 + b = -1.160885976 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 = -1.160885976 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + b = -1.160885976 + 0.3125 b = -1.160885976 + 0.3125 Combine like terms: -1.160885976 + 0.3125 = -0.848385976 b = -0.848385976 Simplifying b = -0.848385976Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.473385976, -0.848385976}
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