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Simplifying 4b2 + -20b + -4 = 0 Reorder the terms: -4 + -20b + 4b2 = 0 Solving -4 + -20b + 4b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + -5b + b2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -5b + b2)' equal to zero and attempt to solve: Simplifying -1 + -5b + b2 = 0 Solving -1 + -5b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -5b + 1 + b2 = 0 + 1 Reorder the terms: -1 + 1 + -5b + b2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5b + b2 = 0 + 1 -5b + b2 = 0 + 1 Combine like terms: 0 + 1 = 1 -5b + b2 = 1 The b term is -5b. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5b + 6.25 + b2 = 1 + 6.25 Reorder the terms: 6.25 + -5b + b2 = 1 + 6.25 Combine like terms: 1 + 6.25 = 7.25 6.25 + -5b + b2 = 7.25 Factor a perfect square on the left side: (b + -2.5)(b + -2.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (b + -2.5) equal to 2.692582404 and -2.692582404.Subproblem 1
b + -2.5 = 2.692582404 Simplifying b + -2.5 = 2.692582404 Reorder the terms: -2.5 + b = 2.692582404 Solving -2.5 + b = 2.692582404 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + b = 2.692582404 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + b = 2.692582404 + 2.5 b = 2.692582404 + 2.5 Combine like terms: 2.692582404 + 2.5 = 5.192582404 b = 5.192582404 Simplifying b = 5.192582404Subproblem 2
b + -2.5 = -2.692582404 Simplifying b + -2.5 = -2.692582404 Reorder the terms: -2.5 + b = -2.692582404 Solving -2.5 + b = -2.692582404 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + b = -2.692582404 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + b = -2.692582404 + 2.5 b = -2.692582404 + 2.5 Combine like terms: -2.692582404 + 2.5 = -0.192582404 b = -0.192582404 Simplifying b = -0.192582404Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.192582404, -0.192582404}Solution
b = {5.192582404, -0.192582404}
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