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Simplifying 4b2 + -8b + 2 = 0 Reorder the terms: 2 + -8b + 4b2 = 0 Solving 2 + -8b + 4b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -4b + 2b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -4b + 2b2)' equal to zero and attempt to solve: Simplifying 1 + -4b + 2b2 = 0 Solving 1 + -4b + 2b2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + -2b + b2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -2b + -0.5 + b2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -2b + b2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -2b + b2 = 0 + -0.5 -2b + b2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -2b + b2 = -0.5 The b term is -2b. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2b + 1 + b2 = -0.5 + 1 Reorder the terms: 1 + -2b + b2 = -0.5 + 1 Combine like terms: -0.5 + 1 = 0.5 1 + -2b + b2 = 0.5 Factor a perfect square on the left side: (b + -1)(b + -1) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (b + -1) equal to 0.707106781 and -0.707106781.Subproblem 1
b + -1 = 0.707106781 Simplifying b + -1 = 0.707106781 Reorder the terms: -1 + b = 0.707106781 Solving -1 + b = 0.707106781 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + b = 0.707106781 + 1 Combine like terms: -1 + 1 = 0 0 + b = 0.707106781 + 1 b = 0.707106781 + 1 Combine like terms: 0.707106781 + 1 = 1.707106781 b = 1.707106781 Simplifying b = 1.707106781Subproblem 2
b + -1 = -0.707106781 Simplifying b + -1 = -0.707106781 Reorder the terms: -1 + b = -0.707106781 Solving -1 + b = -0.707106781 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + b = -0.707106781 + 1 Combine like terms: -1 + 1 = 0 0 + b = -0.707106781 + 1 b = -0.707106781 + 1 Combine like terms: -0.707106781 + 1 = 0.292893219 b = 0.292893219 Simplifying b = 0.292893219Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.707106781, 0.292893219}Solution
b = {1.707106781, 0.292893219}
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