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Simplifying r2 + -22r + 1 = 0 Reorder the terms: 1 + -22r + r2 = 0 Solving 1 + -22r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -22r + -1 + r2 = 0 + -1 Reorder the terms: 1 + -1 + -22r + r2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -22r + r2 = 0 + -1 -22r + r2 = 0 + -1 Combine like terms: 0 + -1 = -1 -22r + r2 = -1 The r term is -22r. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22r + 121 + r2 = -1 + 121 Reorder the terms: 121 + -22r + r2 = -1 + 121 Combine like terms: -1 + 121 = 120 121 + -22r + r2 = 120 Factor a perfect square on the left side: (r + -11)(r + -11) = 120 Calculate the square root of the right side: 10.95445115 Break this problem into two subproblems by setting (r + -11) equal to 10.95445115 and -10.95445115.Subproblem 1
r + -11 = 10.95445115 Simplifying r + -11 = 10.95445115 Reorder the terms: -11 + r = 10.95445115 Solving -11 + r = 10.95445115 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + r = 10.95445115 + 11 Combine like terms: -11 + 11 = 0 0 + r = 10.95445115 + 11 r = 10.95445115 + 11 Combine like terms: 10.95445115 + 11 = 21.95445115 r = 21.95445115 Simplifying r = 21.95445115Subproblem 2
r + -11 = -10.95445115 Simplifying r + -11 = -10.95445115 Reorder the terms: -11 + r = -10.95445115 Solving -11 + r = -10.95445115 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + r = -10.95445115 + 11 Combine like terms: -11 + 11 = 0 0 + r = -10.95445115 + 11 r = -10.95445115 + 11 Combine like terms: -10.95445115 + 11 = 0.04554885 r = 0.04554885 Simplifying r = 0.04554885Solution
The solution to the problem is based on the solutions from the subproblems. r = {21.95445115, 0.04554885}
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