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Simplifying r2 + -4r + 2 = 0 Reorder the terms: 2 + -4r + r2 = 0 Solving 2 + -4r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -4r + -2 + r2 = 0 + -2 Reorder the terms: 2 + -2 + -4r + r2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -4r + r2 = 0 + -2 -4r + r2 = 0 + -2 Combine like terms: 0 + -2 = -2 -4r + r2 = -2 The r term is -4r. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4r + 4 + r2 = -2 + 4 Reorder the terms: 4 + -4r + r2 = -2 + 4 Combine like terms: -2 + 4 = 2 4 + -4r + r2 = 2 Factor a perfect square on the left side: (r + -2)(r + -2) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (r + -2) equal to 1.414213562 and -1.414213562.Subproblem 1
r + -2 = 1.414213562 Simplifying r + -2 = 1.414213562 Reorder the terms: -2 + r = 1.414213562 Solving -2 + r = 1.414213562 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + r = 1.414213562 + 2 Combine like terms: -2 + 2 = 0 0 + r = 1.414213562 + 2 r = 1.414213562 + 2 Combine like terms: 1.414213562 + 2 = 3.414213562 r = 3.414213562 Simplifying r = 3.414213562Subproblem 2
r + -2 = -1.414213562 Simplifying r + -2 = -1.414213562 Reorder the terms: -2 + r = -1.414213562 Solving -2 + r = -1.414213562 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + r = -1.414213562 + 2 Combine like terms: -2 + 2 = 0 0 + r = -1.414213562 + 2 r = -1.414213562 + 2 Combine like terms: -1.414213562 + 2 = 0.585786438 r = 0.585786438 Simplifying r = 0.585786438Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.414213562, 0.585786438}
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