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Simplifying r2 + 2r + -77 = 0 Reorder the terms: -77 + 2r + r2 = 0 Solving -77 + 2r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '77' to each side of the equation. -77 + 2r + 77 + r2 = 0 + 77 Reorder the terms: -77 + 77 + 2r + r2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + 2r + r2 = 0 + 77 2r + r2 = 0 + 77 Combine like terms: 0 + 77 = 77 2r + r2 = 77 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 = 77 + 1 Reorder the terms: 1 + 2r + r2 = 77 + 1 Combine like terms: 77 + 1 = 78 1 + 2r + r2 = 78 Factor a perfect square on the left side: (r + 1)(r + 1) = 78 Calculate the square root of the right side: 8.831760866 Break this problem into two subproblems by setting (r + 1) equal to 8.831760866 and -8.831760866.Subproblem 1
r + 1 = 8.831760866 Simplifying r + 1 = 8.831760866 Reorder the terms: 1 + r = 8.831760866 Solving 1 + r = 8.831760866 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 = 8.831760866 + -1 Combine like terms: 1 + -1 = 0 0 + r = 8.831760866 + -1 r = 8.831760866 + -1 Combine like terms: 8.831760866 + -1 = 7.831760866 r = 7.831760866 Simplifying r = 7.831760866Subproblem 2
r + 1 = -8.831760866 Simplifying r + 1 = -8.831760866 Reorder the terms: 1 + r = -8.831760866 Solving 1 + r = -8.831760866 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 = -8.831760866 + -1 Combine like terms: 1 + -1 = 0 0 + r = -8.831760866 + -1 r = -8.831760866 + -1 Combine like terms: -8.831760866 + -1 = -9.831760866 r = -9.831760866 Simplifying r = -9.831760866Solution
The solution to the problem is based on the solutions from the subproblems. r = {7.831760866, -9.831760866}
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