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Simplifying r2 + 2r + -11 = 0 Reorder the terms: -11 + 2r + r2 = 0 Solving -11 + 2r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 2r + 11 + r2 = 0 + 11 Reorder the terms: -11 + 11 + 2r + r2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 2r + r2 = 0 + 11 2r + r2 = 0 + 11 Combine like terms: 0 + 11 = 11 2r + r2 = 11 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 = 11 + 1 Reorder the terms: 1 + 2r + r2 = 11 + 1 Combine like terms: 11 + 1 = 12 1 + 2r + r2 = 12 Factor a perfect square on the left side: (r + 1)(r + 1) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (r + 1) equal to 3.464101615 and -3.464101615.Subproblem 1
r + 1 = 3.464101615 Simplifying r + 1 = 3.464101615 Reorder the terms: 1 + r = 3.464101615 Solving 1 + r = 3.464101615 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 = 3.464101615 + -1 Combine like terms: 1 + -1 = 0 0 + r = 3.464101615 + -1 r = 3.464101615 + -1 Combine like terms: 3.464101615 + -1 = 2.464101615 r = 2.464101615 Simplifying r = 2.464101615Subproblem 2
r + 1 = -3.464101615 Simplifying r + 1 = -3.464101615 Reorder the terms: 1 + r = -3.464101615 Solving 1 + r = -3.464101615 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 = -3.464101615 + -1 Combine like terms: 1 + -1 = 0 0 + r = -3.464101615 + -1 r = -3.464101615 + -1 Combine like terms: -3.464101615 + -1 = -4.464101615 r = -4.464101615 Simplifying r = -4.464101615Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.464101615, -4.464101615}
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