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Simplifying r2 + -18r + -56 = 0 Reorder the terms: -56 + -18r + r2 = 0 Solving -56 + -18r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + -18r + 56 + r2 = 0 + 56 Reorder the terms: -56 + 56 + -18r + r2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -18r + r2 = 0 + 56 -18r + r2 = 0 + 56 Combine like terms: 0 + 56 = 56 -18r + r2 = 56 The r term is -18r. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18r + 81 + r2 = 56 + 81 Reorder the terms: 81 + -18r + r2 = 56 + 81 Combine like terms: 56 + 81 = 137 81 + -18r + r2 = 137 Factor a perfect square on the left side: (r + -9)(r + -9) = 137 Calculate the square root of the right side: 11.704699911 Break this problem into two subproblems by setting (r + -9) equal to 11.704699911 and -11.704699911.Subproblem 1
r + -9 = 11.704699911 Simplifying r + -9 = 11.704699911 Reorder the terms: -9 + r = 11.704699911 Solving -9 + r = 11.704699911 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + r = 11.704699911 + 9 Combine like terms: -9 + 9 = 0 0 + r = 11.704699911 + 9 r = 11.704699911 + 9 Combine like terms: 11.704699911 + 9 = 20.704699911 r = 20.704699911 Simplifying r = 20.704699911Subproblem 2
r + -9 = -11.704699911 Simplifying r + -9 = -11.704699911 Reorder the terms: -9 + r = -11.704699911 Solving -9 + r = -11.704699911 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + r = -11.704699911 + 9 Combine like terms: -9 + 9 = 0 0 + r = -11.704699911 + 9 r = -11.704699911 + 9 Combine like terms: -11.704699911 + 9 = -2.704699911 r = -2.704699911 Simplifying r = -2.704699911Solution
The solution to the problem is based on the solutions from the subproblems. r = {20.704699911, -2.704699911}
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