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Simplifying 2b2 + 16b = 4 Reorder the terms: 16b + 2b2 = 4 Solving 16b + 2b2 = 4 Solving for variable 'b'. Reorder the terms: -4 + 16b + 2b2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 16b + 2b2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 8b + b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 8b + b2)' equal to zero and attempt to solve: Simplifying -2 + 8b + b2 = 0 Solving -2 + 8b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 8b + 2 + b2 = 0 + 2 Reorder the terms: -2 + 2 + 8b + b2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 8b + b2 = 0 + 2 8b + b2 = 0 + 2 Combine like terms: 0 + 2 = 2 8b + b2 = 2 The b term is 8b. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8b + 16 + b2 = 2 + 16 Reorder the terms: 16 + 8b + b2 = 2 + 16 Combine like terms: 2 + 16 = 18 16 + 8b + b2 = 18 Factor a perfect square on the left side: (b + 4)(b + 4) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (b + 4) equal to 4.242640687 and -4.242640687.Subproblem 1
b + 4 = 4.242640687 Simplifying b + 4 = 4.242640687 Reorder the terms: 4 + b = 4.242640687 Solving 4 + b = 4.242640687 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + b = 4.242640687 + -4 Combine like terms: 4 + -4 = 0 0 + b = 4.242640687 + -4 b = 4.242640687 + -4 Combine like terms: 4.242640687 + -4 = 0.242640687 b = 0.242640687 Simplifying b = 0.242640687Subproblem 2
b + 4 = -4.242640687 Simplifying b + 4 = -4.242640687 Reorder the terms: 4 + b = -4.242640687 Solving 4 + b = -4.242640687 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + b = -4.242640687 + -4 Combine like terms: 4 + -4 = 0 0 + b = -4.242640687 + -4 b = -4.242640687 + -4 Combine like terms: -4.242640687 + -4 = -8.242640687 b = -8.242640687 Simplifying b = -8.242640687Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.242640687, -8.242640687}Solution
b = {0.242640687, -8.242640687}
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