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Simplifying 4b2 + -5b + -5 = 0 Reorder the terms: -5 + -5b + 4b2 = 0 Solving -5 + -5b + 4b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -1.25b + b2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -1.25b + 1.25 + b2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -1.25b + b2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -1.25b + b2 = 0 + 1.25 -1.25b + b2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -1.25b + b2 = 1.25 The b term is -1.25b. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25b + 0.390625 + b2 = 1.25 + 0.390625 Reorder the terms: 0.390625 + -1.25b + b2 = 1.25 + 0.390625 Combine like terms: 1.25 + 0.390625 = 1.640625 0.390625 + -1.25b + b2 = 1.640625 Factor a perfect square on the left side: (b + -0.625)(b + -0.625) = 1.640625 Calculate the square root of the right side: 1.280868846 Break this problem into two subproblems by setting (b + -0.625) equal to 1.280868846 and -1.280868846.Subproblem 1
b + -0.625 = 1.280868846 Simplifying b + -0.625 = 1.280868846 Reorder the terms: -0.625 + b = 1.280868846 Solving -0.625 + b = 1.280868846 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + b = 1.280868846 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + b = 1.280868846 + 0.625 b = 1.280868846 + 0.625 Combine like terms: 1.280868846 + 0.625 = 1.905868846 b = 1.905868846 Simplifying b = 1.905868846Subproblem 2
b + -0.625 = -1.280868846 Simplifying b + -0.625 = -1.280868846 Reorder the terms: -0.625 + b = -1.280868846 Solving -0.625 + b = -1.280868846 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + b = -1.280868846 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + b = -1.280868846 + 0.625 b = -1.280868846 + 0.625 Combine like terms: -1.280868846 + 0.625 = -0.655868846 b = -0.655868846 Simplifying b = -0.655868846Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.905868846, -0.655868846}
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