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Simplifying b2 + -1b + -6 = 8 Reorder the terms: -6 + -1b + b2 = 8 Solving -6 + -1b + b2 = 8 Solving for variable 'b'. Reorder the terms: -6 + -8 + -1b + b2 = 8 + -8 Combine like terms: -6 + -8 = -14 -14 + -1b + b2 = 8 + -8 Combine like terms: 8 + -8 = 0 -14 + -1b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -1b + 14 + b2 = 0 + 14 Reorder the terms: -14 + 14 + -1b + b2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -1b + b2 = 0 + 14 -1b + b2 = 0 + 14 Combine like terms: 0 + 14 = 14 -1b + b2 = 14 The b term is -1b. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1b + 0.25 + b2 = 14 + 0.25 Reorder the terms: 0.25 + -1b + b2 = 14 + 0.25 Combine like terms: 14 + 0.25 = 14.25 0.25 + -1b + b2 = 14.25 Factor a perfect square on the left side: (b + -0.5)(b + -0.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (b + -0.5) equal to 3.774917218 and -3.774917218.Subproblem 1
b + -0.5 = 3.774917218 Simplifying b + -0.5 = 3.774917218 Reorder the terms: -0.5 + b = 3.774917218 Solving -0.5 + b = 3.774917218 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + b = 3.774917218 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + b = 3.774917218 + 0.5 b = 3.774917218 + 0.5 Combine like terms: 3.774917218 + 0.5 = 4.274917218 b = 4.274917218 Simplifying b = 4.274917218Subproblem 2
b + -0.5 = -3.774917218 Simplifying b + -0.5 = -3.774917218 Reorder the terms: -0.5 + b = -3.774917218 Solving -0.5 + b = -3.774917218 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + b = -3.774917218 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + b = -3.774917218 + 0.5 b = -3.774917218 + 0.5 Combine like terms: -3.774917218 + 0.5 = -3.274917218 b = -3.274917218 Simplifying b = -3.274917218Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.274917218, -3.274917218}
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