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Simplifying r2 + -1r + -1r + -20 = 0 Reorder the terms: -20 + -1r + -1r + r2 = 0 Combine like terms: -1r + -1r = -2r -20 + -2r + r2 = 0 Solving -20 + -2r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -2r + 20 + r2 = 0 + 20 Reorder the terms: -20 + 20 + -2r + r2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -2r + r2 = 0 + 20 -2r + r2 = 0 + 20 Combine like terms: 0 + 20 = 20 -2r + r2 = 20 The r term is -2r. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2r + 1 + r2 = 20 + 1 Reorder the terms: 1 + -2r + r2 = 20 + 1 Combine like terms: 20 + 1 = 21 1 + -2r + r2 = 21 Factor a perfect square on the left side: (r + -1)(r + -1) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (r + -1) equal to 4.582575695 and -4.582575695.Subproblem 1
r + -1 = 4.582575695 Simplifying r + -1 = 4.582575695 Reorder the terms: -1 + r = 4.582575695 Solving -1 + r = 4.582575695 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + r = 4.582575695 + 1 Combine like terms: -1 + 1 = 0 0 + r = 4.582575695 + 1 r = 4.582575695 + 1 Combine like terms: 4.582575695 + 1 = 5.582575695 r = 5.582575695 Simplifying r = 5.582575695Subproblem 2
r + -1 = -4.582575695 Simplifying r + -1 = -4.582575695 Reorder the terms: -1 + r = -4.582575695 Solving -1 + r = -4.582575695 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + r = -4.582575695 + 1 Combine like terms: -1 + 1 = 0 0 + r = -4.582575695 + 1 r = -4.582575695 + 1 Combine like terms: -4.582575695 + 1 = -3.582575695 r = -3.582575695 Simplifying r = -3.582575695Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.582575695, -3.582575695}
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