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Simplifying r2 + -9r + -38 = -29 Reorder the terms: -38 + -9r + r2 = -29 Solving -38 + -9r + r2 = -29 Solving for variable 'r'. Reorder the terms: -38 + 29 + -9r + r2 = -29 + 29 Combine like terms: -38 + 29 = -9 -9 + -9r + r2 = -29 + 29 Combine like terms: -29 + 29 = 0 -9 + -9r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -9r + 9 + r2 = 0 + 9 Reorder the terms: -9 + 9 + -9r + r2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -9r + r2 = 0 + 9 -9r + r2 = 0 + 9 Combine like terms: 0 + 9 = 9 -9r + r2 = 9 The r term is -9r. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9r + 20.25 + r2 = 9 + 20.25 Reorder the terms: 20.25 + -9r + r2 = 9 + 20.25 Combine like terms: 9 + 20.25 = 29.25 20.25 + -9r + r2 = 29.25 Factor a perfect square on the left side: (r + -4.5)(r + -4.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (r + -4.5) equal to 5.408326913 and -5.408326913.Subproblem 1
r + -4.5 = 5.408326913 Simplifying r + -4.5 = 5.408326913 Reorder the terms: -4.5 + r = 5.408326913 Solving -4.5 + r = 5.408326913 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + r = 5.408326913 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + r = 5.408326913 + 4.5 r = 5.408326913 + 4.5 Combine like terms: 5.408326913 + 4.5 = 9.908326913 r = 9.908326913 Simplifying r = 9.908326913Subproblem 2
r + -4.5 = -5.408326913 Simplifying r + -4.5 = -5.408326913 Reorder the terms: -4.5 + r = -5.408326913 Solving -4.5 + r = -5.408326913 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + r = -5.408326913 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + r = -5.408326913 + 4.5 r = -5.408326913 + 4.5 Combine like terms: -5.408326913 + 4.5 = -0.908326913 r = -0.908326913 Simplifying r = -0.908326913Solution
The solution to the problem is based on the solutions from the subproblems. r = {9.908326913, -0.908326913}
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