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Simplifying (b + -3)(b + -3) = 6 Reorder the terms: (-3 + b)(b + -3) = 6 Reorder the terms: (-3 + b)(-3 + b) = 6 Multiply (-3 + b) * (-3 + b) (-3(-3 + b) + b(-3 + b)) = 6 ((-3 * -3 + b * -3) + b(-3 + b)) = 6 ((9 + -3b) + b(-3 + b)) = 6 (9 + -3b + (-3 * b + b * b)) = 6 (9 + -3b + (-3b + b2)) = 6 Combine like terms: -3b + -3b = -6b (9 + -6b + b2) = 6 Solving 9 + -6b + b2 = 6 Solving for variable 'b'. Reorder the terms: 9 + -6 + -6b + b2 = 6 + -6 Combine like terms: 9 + -6 = 3 3 + -6b + b2 = 6 + -6 Combine like terms: 6 + -6 = 0 3 + -6b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -6b + -3 + b2 = 0 + -3 Reorder the terms: 3 + -3 + -6b + b2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -6b + b2 = 0 + -3 -6b + b2 = 0 + -3 Combine like terms: 0 + -3 = -3 -6b + b2 = -3 The b term is -6b. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6b + 9 + b2 = -3 + 9 Reorder the terms: 9 + -6b + b2 = -3 + 9 Combine like terms: -3 + 9 = 6 9 + -6b + b2 = 6 Factor a perfect square on the left side: (b + -3)(b + -3) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (b + -3) equal to 2.449489743 and -2.449489743.Subproblem 1
b + -3 = 2.449489743 Simplifying b + -3 = 2.449489743 Reorder the terms: -3 + b = 2.449489743 Solving -3 + b = 2.449489743 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + b = 2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + b = 2.449489743 + 3 b = 2.449489743 + 3 Combine like terms: 2.449489743 + 3 = 5.449489743 b = 5.449489743 Simplifying b = 5.449489743Subproblem 2
b + -3 = -2.449489743 Simplifying b + -3 = -2.449489743 Reorder the terms: -3 + b = -2.449489743 Solving -3 + b = -2.449489743 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + b = -2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + b = -2.449489743 + 3 b = -2.449489743 + 3 Combine like terms: -2.449489743 + 3 = 0.550510257 b = 0.550510257 Simplifying b = 0.550510257Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.449489743, 0.550510257}
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