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Simplifying r2 + 26r = 49 Reorder the terms: 26r + r2 = 49 Solving 26r + r2 = 49 Solving for variable 'r'. Reorder the terms: -49 + 26r + r2 = 49 + -49 Combine like terms: 49 + -49 = 0 -49 + 26r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 26r + 49 + r2 = 0 + 49 Reorder the terms: -49 + 49 + 26r + r2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 26r + r2 = 0 + 49 26r + r2 = 0 + 49 Combine like terms: 0 + 49 = 49 26r + r2 = 49 The r term is 26r. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26r + 169 + r2 = 49 + 169 Reorder the terms: 169 + 26r + r2 = 49 + 169 Combine like terms: 49 + 169 = 218 169 + 26r + r2 = 218 Factor a perfect square on the left side: (r + 13)(r + 13) = 218 Calculate the square root of the right side: 14.76482306 Break this problem into two subproblems by setting (r + 13) equal to 14.76482306 and -14.76482306.Subproblem 1
r + 13 = 14.76482306 Simplifying r + 13 = 14.76482306 Reorder the terms: 13 + r = 14.76482306 Solving 13 + r = 14.76482306 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + r = 14.76482306 + -13 Combine like terms: 13 + -13 = 0 0 + r = 14.76482306 + -13 r = 14.76482306 + -13 Combine like terms: 14.76482306 + -13 = 1.76482306 r = 1.76482306 Simplifying r = 1.76482306Subproblem 2
r + 13 = -14.76482306 Simplifying r + 13 = -14.76482306 Reorder the terms: 13 + r = -14.76482306 Solving 13 + r = -14.76482306 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + r = -14.76482306 + -13 Combine like terms: 13 + -13 = 0 0 + r = -14.76482306 + -13 r = -14.76482306 + -13 Combine like terms: -14.76482306 + -13 = -27.76482306 r = -27.76482306 Simplifying r = -27.76482306Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.76482306, -27.76482306}
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