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Simplifying r2 + 2r + -69.23 = 0 Reorder the terms: -69.23 + 2r + r2 = 0 Solving -69.23 + 2r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '69.23' to each side of the equation. -69.23 + 2r + 69.23 + r2 = 0 + 69.23 Reorder the terms: -69.23 + 69.23 + 2r + r2 = 0 + 69.23 Combine like terms: -69.23 + 69.23 = 0.00 0.00 + 2r + r2 = 0 + 69.23 2r + r2 = 0 + 69.23 Combine like terms: 0 + 69.23 = 69.23 2r + r2 = 69.23 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 = 69.23 + 1 Reorder the terms: 1 + 2r + r2 = 69.23 + 1 Combine like terms: 69.23 + 1 = 70.23 1 + 2r + r2 = 70.23 Factor a perfect square on the left side: (r + 1)(r + 1) = 70.23 Calculate the square root of the right side: 8.380334122 Break this problem into two subproblems by setting (r + 1) equal to 8.380334122 and -8.380334122.Subproblem 1
r + 1 = 8.380334122 Simplifying r + 1 = 8.380334122 Reorder the terms: 1 + r = 8.380334122 Solving 1 + r = 8.380334122 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 = 8.380334122 + -1 Combine like terms: 1 + -1 = 0 0 + r = 8.380334122 + -1 r = 8.380334122 + -1 Combine like terms: 8.380334122 + -1 = 7.380334122 r = 7.380334122 Simplifying r = 7.380334122Subproblem 2
r + 1 = -8.380334122 Simplifying r + 1 = -8.380334122 Reorder the terms: 1 + r = -8.380334122 Solving 1 + r = -8.380334122 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 = -8.380334122 + -1 Combine like terms: 1 + -1 = 0 0 + r = -8.380334122 + -1 r = -8.380334122 + -1 Combine like terms: -8.380334122 + -1 = -9.380334122 r = -9.380334122 Simplifying r = -9.380334122Solution
The solution to the problem is based on the solutions from the subproblems. r = {7.380334122, -9.380334122}
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