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Simplifying 22b2 + b + -30 = 0 Reorder the terms: -30 + b + 22b2 = 0 Solving -30 + b + 22b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 22 the coefficient of the squared term: Divide each side by '22'. -1.363636364 + 0.04545454545b + b2 = 0 Move the constant term to the right: Add '1.363636364' to each side of the equation. -1.363636364 + 0.04545454545b + 1.363636364 + b2 = 0 + 1.363636364 Reorder the terms: -1.363636364 + 1.363636364 + 0.04545454545b + b2 = 0 + 1.363636364 Combine like terms: -1.363636364 + 1.363636364 = 0.000000000 0.000000000 + 0.04545454545b + b2 = 0 + 1.363636364 0.04545454545b + b2 = 0 + 1.363636364 Combine like terms: 0 + 1.363636364 = 1.363636364 0.04545454545b + b2 = 1.363636364 The b term is b. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.04545454545b + 0.25 + b2 = 1.363636364 + 0.25 Reorder the terms: 0.25 + 0.04545454545b + b2 = 1.363636364 + 0.25 Combine like terms: 1.363636364 + 0.25 = 1.613636364 0.25 + 0.04545454545b + b2 = 1.613636364 Factor a perfect square on the left side: (b + 0.5)(b + 0.5) = 1.613636364 Calculate the square root of the right side: 1.270289874 Break this problem into two subproblems by setting (b + 0.5) equal to 1.270289874 and -1.270289874.Subproblem 1
b + 0.5 = 1.270289874 Simplifying b + 0.5 = 1.270289874 Reorder the terms: 0.5 + b = 1.270289874 Solving 0.5 + b = 1.270289874 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + b = 1.270289874 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = 1.270289874 + -0.5 b = 1.270289874 + -0.5 Combine like terms: 1.270289874 + -0.5 = 0.770289874 b = 0.770289874 Simplifying b = 0.770289874Subproblem 2
b + 0.5 = -1.270289874 Simplifying b + 0.5 = -1.270289874 Reorder the terms: 0.5 + b = -1.270289874 Solving 0.5 + b = -1.270289874 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + b = -1.270289874 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = -1.270289874 + -0.5 b = -1.270289874 + -0.5 Combine like terms: -1.270289874 + -0.5 = -1.770289874 b = -1.770289874 Simplifying b = -1.770289874Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.770289874, -1.770289874}
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