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Simplifying r2 + -18r + 56 = 0 + -4 Reorder the terms: 56 + -18r + r2 = 0 + -4 Combine like terms: 0 + -4 = -4 56 + -18r + r2 = -4 Solving 56 + -18r + r2 = -4 Solving for variable 'r'. Reorder the terms: 56 + 4 + -18r + r2 = -4 + 4 Combine like terms: 56 + 4 = 60 60 + -18r + r2 = -4 + 4 Combine like terms: -4 + 4 = 0 60 + -18r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + -18r + -60 + r2 = 0 + -60 Reorder the terms: 60 + -60 + -18r + r2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -18r + r2 = 0 + -60 -18r + r2 = 0 + -60 Combine like terms: 0 + -60 = -60 -18r + r2 = -60 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 = -60 + 81 Reorder the terms: 81 + -18r + r2 = -60 + 81 Combine like terms: -60 + 81 = 21 81 + -18r + r2 = 21 Factor a perfect square on the left side: (r + -9)(r + -9) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (r + -9) equal to 4.582575695 and -4.582575695.Subproblem 1
r + -9 = 4.582575695 Simplifying r + -9 = 4.582575695 Reorder the terms: -9 + r = 4.582575695 Solving -9 + r = 4.582575695 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 = 4.582575695 + 9 Combine like terms: -9 + 9 = 0 0 + r = 4.582575695 + 9 r = 4.582575695 + 9 Combine like terms: 4.582575695 + 9 = 13.582575695 r = 13.582575695 Simplifying r = 13.582575695Subproblem 2
r + -9 = -4.582575695 Simplifying r + -9 = -4.582575695 Reorder the terms: -9 + r = -4.582575695 Solving -9 + r = -4.582575695 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 = -4.582575695 + 9 Combine like terms: -9 + 9 = 0 0 + r = -4.582575695 + 9 r = -4.582575695 + 9 Combine like terms: -4.582575695 + 9 = 4.417424305 r = 4.417424305 Simplifying r = 4.417424305Solution
The solution to the problem is based on the solutions from the subproblems. r = {13.582575695, 4.417424305}
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