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Simplifying 8b2 + 16b + 4 = 8 Reorder the terms: 4 + 16b + 8b2 = 8 Solving 4 + 16b + 8b2 = 8 Solving for variable 'b'. Reorder the terms: 4 + -8 + 16b + 8b2 = 8 + -8 Combine like terms: 4 + -8 = -4 -4 + 16b + 8b2 = 8 + -8 Combine like terms: 8 + -8 = 0 -4 + 16b + 8b2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + 4b + 2b2) = 0 Ignore the factor 4.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 = 1.5 1 + 2b + b2 = 1.5 Factor a perfect square on the left side: (b + 1)(b + 1) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (b + 1) equal to 1.224744871 and -1.224744871.Subproblem 1
b + 1 = 1.224744871 Simplifying b + 1 = 1.224744871 Reorder the terms: 1 + b = 1.224744871 Solving 1 + b = 1.224744871 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 = 1.224744871 + -1 Combine like terms: 1 + -1 = 0 0 + b = 1.224744871 + -1 b = 1.224744871 + -1 Combine like terms: 1.224744871 + -1 = 0.224744871 b = 0.224744871 Simplifying b = 0.224744871Subproblem 2
b + 1 = -1.224744871 Simplifying b + 1 = -1.224744871 Reorder the terms: 1 + b = -1.224744871 Solving 1 + b = -1.224744871 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 = -1.224744871 + -1 Combine like terms: 1 + -1 = 0 0 + b = -1.224744871 + -1 b = -1.224744871 + -1 Combine like terms: -1.224744871 + -1 = -2.224744871 b = -2.224744871 Simplifying b = -2.224744871Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.224744871, -2.224744871}Solution
b = {0.224744871, -2.224744871}
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