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Simplifying r2 + -5r + 1 = 0 Reorder the terms: 1 + -5r + r2 = 0 Solving 1 + -5r + 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 + -5r + -1 + r2 = 0 + -1 Reorder the terms: 1 + -1 + -5r + r2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5r + r2 = 0 + -1 -5r + r2 = 0 + -1 Combine like terms: 0 + -1 = -1 -5r + r2 = -1 The r term is -5r. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5r + 6.25 + r2 = -1 + 6.25 Reorder the terms: 6.25 + -5r + r2 = -1 + 6.25 Combine like terms: -1 + 6.25 = 5.25 6.25 + -5r + r2 = 5.25 Factor a perfect square on the left side: (r + -2.5)(r + -2.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (r + -2.5) equal to 2.291287847 and -2.291287847.Subproblem 1
r + -2.5 = 2.291287847 Simplifying r + -2.5 = 2.291287847 Reorder the terms: -2.5 + r = 2.291287847 Solving -2.5 + r = 2.291287847 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + r = 2.291287847 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + r = 2.291287847 + 2.5 r = 2.291287847 + 2.5 Combine like terms: 2.291287847 + 2.5 = 4.791287847 r = 4.791287847 Simplifying r = 4.791287847Subproblem 2
r + -2.5 = -2.291287847 Simplifying r + -2.5 = -2.291287847 Reorder the terms: -2.5 + r = -2.291287847 Solving -2.5 + r = -2.291287847 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + r = -2.291287847 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + r = -2.291287847 + 2.5 r = -2.291287847 + 2.5 Combine like terms: -2.291287847 + 2.5 = 0.208712153 r = 0.208712153 Simplifying r = 0.208712153Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.791287847, 0.208712153}
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