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Simplifying 2r2 + 8r + 5 = 0 Reorder the terms: 5 + 8r + 2r2 = 0 Solving 5 + 8r + 2r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + 4r + r2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 4r + -2.5 + r2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 4r + r2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 4r + r2 = 0 + -2.5 4r + r2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 4r + r2 = -2.5 The r term is 4r. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4r + 4 + r2 = -2.5 + 4 Reorder the terms: 4 + 4r + r2 = -2.5 + 4 Combine like terms: -2.5 + 4 = 1.5 4 + 4r + r2 = 1.5 Factor a perfect square on the left side: (r + 2)(r + 2) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (r + 2) equal to 1.224744871 and -1.224744871.Subproblem 1
r + 2 = 1.224744871 Simplifying r + 2 = 1.224744871 Reorder the terms: 2 + r = 1.224744871 Solving 2 + r = 1.224744871 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = 1.224744871 + -2 Combine like terms: 2 + -2 = 0 0 + r = 1.224744871 + -2 r = 1.224744871 + -2 Combine like terms: 1.224744871 + -2 = -0.775255129 r = -0.775255129 Simplifying r = -0.775255129Subproblem 2
r + 2 = -1.224744871 Simplifying r + 2 = -1.224744871 Reorder the terms: 2 + r = -1.224744871 Solving 2 + r = -1.224744871 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = -1.224744871 + -2 Combine like terms: 2 + -2 = 0 0 + r = -1.224744871 + -2 r = -1.224744871 + -2 Combine like terms: -1.224744871 + -2 = -3.224744871 r = -3.224744871 Simplifying r = -3.224744871Solution
The solution to the problem is based on the solutions from the subproblems. r = {-0.775255129, -3.224744871}
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