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Simplifying r2 + 28r = 11 Reorder the terms: 28r + r2 = 11 Solving 28r + r2 = 11 Solving for variable 'r'. Reorder the terms: -11 + 28r + r2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 28r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 28r + 11 + r2 = 0 + 11 Reorder the terms: -11 + 11 + 28r + r2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 28r + r2 = 0 + 11 28r + r2 = 0 + 11 Combine like terms: 0 + 11 = 11 28r + r2 = 11 The r term is 28r. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28r + 196 + r2 = 11 + 196 Reorder the terms: 196 + 28r + r2 = 11 + 196 Combine like terms: 11 + 196 = 207 196 + 28r + r2 = 207 Factor a perfect square on the left side: (r + 14)(r + 14) = 207 Calculate the square root of the right side: 14.38749457 Break this problem into two subproblems by setting (r + 14) equal to 14.38749457 and -14.38749457.Subproblem 1
r + 14 = 14.38749457 Simplifying r + 14 = 14.38749457 Reorder the terms: 14 + r = 14.38749457 Solving 14 + r = 14.38749457 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + r = 14.38749457 + -14 Combine like terms: 14 + -14 = 0 0 + r = 14.38749457 + -14 r = 14.38749457 + -14 Combine like terms: 14.38749457 + -14 = 0.38749457 r = 0.38749457 Simplifying r = 0.38749457Subproblem 2
r + 14 = -14.38749457 Simplifying r + 14 = -14.38749457 Reorder the terms: 14 + r = -14.38749457 Solving 14 + r = -14.38749457 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + r = -14.38749457 + -14 Combine like terms: 14 + -14 = 0 0 + r = -14.38749457 + -14 r = -14.38749457 + -14 Combine like terms: -14.38749457 + -14 = -28.38749457 r = -28.38749457 Simplifying r = -28.38749457Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.38749457, -28.38749457}
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