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Simplifying R2 + 2R + -1 = 0 Reorder the terms: -1 + 2R + R2 = 0 Solving -1 + 2R + 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 + 2R + 1 + R2 = 0 + 1 Reorder the terms: -1 + 1 + 2R + R2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2R + R2 = 0 + 1 2R + R2 = 0 + 1 Combine like terms: 0 + 1 = 1 2R + R2 = 1 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 = 1 + 1 Reorder the terms: 1 + 2R + R2 = 1 + 1 Combine like terms: 1 + 1 = 2 1 + 2R + R2 = 2 Factor a perfect square on the left side: (R + 1)(R + 1) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (R + 1) equal to 1.414213562 and -1.414213562.Subproblem 1
R + 1 = 1.414213562 Simplifying R + 1 = 1.414213562 Reorder the terms: 1 + R = 1.414213562 Solving 1 + R = 1.414213562 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 = 1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + R = 1.414213562 + -1 R = 1.414213562 + -1 Combine like terms: 1.414213562 + -1 = 0.414213562 R = 0.414213562 Simplifying R = 0.414213562Subproblem 2
R + 1 = -1.414213562 Simplifying R + 1 = -1.414213562 Reorder the terms: 1 + R = -1.414213562 Solving 1 + R = -1.414213562 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 = -1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + R = -1.414213562 + -1 R = -1.414213562 + -1 Combine like terms: -1.414213562 + -1 = -2.414213562 R = -2.414213562 Simplifying R = -2.414213562Solution
The solution to the problem is based on the solutions from the subproblems. R = {0.414213562, -2.414213562}
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