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Simplifying b2 + -10b + -5 = 0 Reorder the terms: -5 + -10b + b2 = 0 Solving -5 + -10b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -10b + 5 + b2 = 0 + 5 Reorder the terms: -5 + 5 + -10b + b2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -10b + b2 = 0 + 5 -10b + b2 = 0 + 5 Combine like terms: 0 + 5 = 5 -10b + b2 = 5 The b term is -10b. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10b + 25 + b2 = 5 + 25 Reorder the terms: 25 + -10b + b2 = 5 + 25 Combine like terms: 5 + 25 = 30 25 + -10b + b2 = 30 Factor a perfect square on the left side: (b + -5)(b + -5) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (b + -5) equal to 5.477225575 and -5.477225575.Subproblem 1
b + -5 = 5.477225575 Simplifying b + -5 = 5.477225575 Reorder the terms: -5 + b = 5.477225575 Solving -5 + b = 5.477225575 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + b = 5.477225575 + 5 Combine like terms: -5 + 5 = 0 0 + b = 5.477225575 + 5 b = 5.477225575 + 5 Combine like terms: 5.477225575 + 5 = 10.477225575 b = 10.477225575 Simplifying b = 10.477225575Subproblem 2
b + -5 = -5.477225575 Simplifying b + -5 = -5.477225575 Reorder the terms: -5 + b = -5.477225575 Solving -5 + b = -5.477225575 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + b = -5.477225575 + 5 Combine like terms: -5 + 5 = 0 0 + b = -5.477225575 + 5 b = -5.477225575 + 5 Combine like terms: -5.477225575 + 5 = -0.477225575 b = -0.477225575 Simplifying b = -0.477225575Solution
The solution to the problem is based on the solutions from the subproblems. b = {10.477225575, -0.477225575}
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