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Simplifying 4b2 + -2b + -16 = 0 Reorder the terms: -16 + -2b + 4b2 = 0 Solving -16 + -2b + 4b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + -1b + 2b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + -1b + 2b2)' equal to zero and attempt to solve: Simplifying -8 + -1b + 2b2 = 0 Solving -8 + -1b + 2b2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4 + -0.5b + b2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -0.5b + 4 + b2 = 0 + 4 Reorder the terms: -4 + 4 + -0.5b + b2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -0.5b + b2 = 0 + 4 -0.5b + b2 = 0 + 4 Combine like terms: 0 + 4 = 4 -0.5b + b2 = 4 The b term is -0.5b. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5b + 0.0625 + b2 = 4 + 0.0625 Reorder the terms: 0.0625 + -0.5b + b2 = 4 + 0.0625 Combine like terms: 4 + 0.0625 = 4.0625 0.0625 + -0.5b + b2 = 4.0625 Factor a perfect square on the left side: (b + -0.25)(b + -0.25) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (b + -0.25) equal to 2.015564437 and -2.015564437.Subproblem 1
b + -0.25 = 2.015564437 Simplifying b + -0.25 = 2.015564437 Reorder the terms: -0.25 + b = 2.015564437 Solving -0.25 + b = 2.015564437 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + b = 2.015564437 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + b = 2.015564437 + 0.25 b = 2.015564437 + 0.25 Combine like terms: 2.015564437 + 0.25 = 2.265564437 b = 2.265564437 Simplifying b = 2.265564437Subproblem 2
b + -0.25 = -2.015564437 Simplifying b + -0.25 = -2.015564437 Reorder the terms: -0.25 + b = -2.015564437 Solving -0.25 + b = -2.015564437 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + b = -2.015564437 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + b = -2.015564437 + 0.25 b = -2.015564437 + 0.25 Combine like terms: -2.015564437 + 0.25 = -1.765564437 b = -1.765564437 Simplifying b = -1.765564437Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.265564437, -1.765564437}Solution
b = {2.265564437, -1.765564437}
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