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Simplifying r2 + 2r + -110 = 0 Reorder the terms: -110 + 2r + r2 = 0 Solving -110 + 2r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '110' to each side of the equation. -110 + 2r + 110 + r2 = 0 + 110 Reorder the terms: -110 + 110 + 2r + r2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + 2r + r2 = 0 + 110 2r + r2 = 0 + 110 Combine like terms: 0 + 110 = 110 2r + r2 = 110 The r term is 2r. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2r + 1 + r2 = 110 + 1 Reorder the terms: 1 + 2r + r2 = 110 + 1 Combine like terms: 110 + 1 = 111 1 + 2r + r2 = 111 Factor a perfect square on the left side: (r + 1)(r + 1) = 111 Calculate the square root of the right side: 10.535653753 Break this problem into two subproblems by setting (r + 1) equal to 10.535653753 and -10.535653753.Subproblem 1
r + 1 = 10.535653753 Simplifying r + 1 = 10.535653753 Reorder the terms: 1 + r = 10.535653753 Solving 1 + r = 10.535653753 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = 10.535653753 + -1 Combine like terms: 1 + -1 = 0 0 + r = 10.535653753 + -1 r = 10.535653753 + -1 Combine like terms: 10.535653753 + -1 = 9.535653753 r = 9.535653753 Simplifying r = 9.535653753Subproblem 2
r + 1 = -10.535653753 Simplifying r + 1 = -10.535653753 Reorder the terms: 1 + r = -10.535653753 Solving 1 + r = -10.535653753 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = -10.535653753 + -1 Combine like terms: 1 + -1 = 0 0 + r = -10.535653753 + -1 r = -10.535653753 + -1 Combine like terms: -10.535653753 + -1 = -11.535653753 r = -11.535653753 Simplifying r = -11.535653753Solution
The solution to the problem is based on the solutions from the subproblems. r = {9.535653753, -11.535653753}
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