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Simplifying 4b2 = -5 + 11b Solving 4b2 = -5 + 11b Solving for variable 'b'. Reorder the terms: 5 + -11b + 4b2 = -5 + 11b + 5 + -11b Reorder the terms: 5 + -11b + 4b2 = -5 + 5 + 11b + -11b Combine like terms: -5 + 5 = 0 5 + -11b + 4b2 = 0 + 11b + -11b 5 + -11b + 4b2 = 11b + -11b Combine like terms: 11b + -11b = 0 5 + -11b + 4b2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + -2.75b + b2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -2.75b + -1.25 + b2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -2.75b + b2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -2.75b + b2 = 0 + -1.25 -2.75b + b2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -2.75b + b2 = -1.25 The b term is -2.75b. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75b + 1.890625 + b2 = -1.25 + 1.890625 Reorder the terms: 1.890625 + -2.75b + b2 = -1.25 + 1.890625 Combine like terms: -1.25 + 1.890625 = 0.640625 1.890625 + -2.75b + b2 = 0.640625 Factor a perfect square on the left side: (b + -1.375)(b + -1.375) = 0.640625 Calculate the square root of the right side: 0.80039053 Break this problem into two subproblems by setting (b + -1.375) equal to 0.80039053 and -0.80039053.Subproblem 1
b + -1.375 = 0.80039053 Simplifying b + -1.375 = 0.80039053 Reorder the terms: -1.375 + b = 0.80039053 Solving -1.375 + b = 0.80039053 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + b = 0.80039053 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + b = 0.80039053 + 1.375 b = 0.80039053 + 1.375 Combine like terms: 0.80039053 + 1.375 = 2.17539053 b = 2.17539053 Simplifying b = 2.17539053Subproblem 2
b + -1.375 = -0.80039053 Simplifying b + -1.375 = -0.80039053 Reorder the terms: -1.375 + b = -0.80039053 Solving -1.375 + b = -0.80039053 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + b = -0.80039053 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + b = -0.80039053 + 1.375 b = -0.80039053 + 1.375 Combine like terms: -0.80039053 + 1.375 = 0.57460947 b = 0.57460947 Simplifying b = 0.57460947Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.17539053, 0.57460947}
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