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Simplifying r2 + 5r = 11 Reorder the terms: 5r + r2 = 11 Solving 5r + r2 = 11 Solving for variable 'r'. Reorder the terms: -11 + 5r + r2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 5r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 5r + 11 + r2 = 0 + 11 Reorder the terms: -11 + 11 + 5r + r2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 5r + r2 = 0 + 11 5r + r2 = 0 + 11 Combine like terms: 0 + 11 = 11 5r + r2 = 11 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 = 11 + 6.25 Reorder the terms: 6.25 + 5r + r2 = 11 + 6.25 Combine like terms: 11 + 6.25 = 17.25 6.25 + 5r + r2 = 17.25 Factor a perfect square on the left side: (r + 2.5)(r + 2.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (r + 2.5) equal to 4.153311931 and -4.153311931.Subproblem 1
r + 2.5 = 4.153311931 Simplifying r + 2.5 = 4.153311931 Reorder the terms: 2.5 + r = 4.153311931 Solving 2.5 + r = 4.153311931 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 = 4.153311931 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + r = 4.153311931 + -2.5 r = 4.153311931 + -2.5 Combine like terms: 4.153311931 + -2.5 = 1.653311931 r = 1.653311931 Simplifying r = 1.653311931Subproblem 2
r + 2.5 = -4.153311931 Simplifying r + 2.5 = -4.153311931 Reorder the terms: 2.5 + r = -4.153311931 Solving 2.5 + r = -4.153311931 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 = -4.153311931 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + r = -4.153311931 + -2.5 r = -4.153311931 + -2.5 Combine like terms: -4.153311931 + -2.5 = -6.653311931 r = -6.653311931 Simplifying r = -6.653311931Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.653311931, -6.653311931}
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