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Simplifying r2 + -6r + -71 = 0 Reorder the terms: -71 + -6r + r2 = 0 Solving -71 + -6r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '71' to each side of the equation. -71 + -6r + 71 + r2 = 0 + 71 Reorder the terms: -71 + 71 + -6r + r2 = 0 + 71 Combine like terms: -71 + 71 = 0 0 + -6r + r2 = 0 + 71 -6r + r2 = 0 + 71 Combine like terms: 0 + 71 = 71 -6r + r2 = 71 The r term is -6r. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6r + 9 + r2 = 71 + 9 Reorder the terms: 9 + -6r + r2 = 71 + 9 Combine like terms: 71 + 9 = 80 9 + -6r + r2 = 80 Factor a perfect square on the left side: (r + -3)(r + -3) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (r + -3) equal to 8.94427191 and -8.94427191.Subproblem 1
r + -3 = 8.94427191 Simplifying r + -3 = 8.94427191 Reorder the terms: -3 + r = 8.94427191 Solving -3 + r = 8.94427191 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + r = 8.94427191 + 3 Combine like terms: -3 + 3 = 0 0 + r = 8.94427191 + 3 r = 8.94427191 + 3 Combine like terms: 8.94427191 + 3 = 11.94427191 r = 11.94427191 Simplifying r = 11.94427191Subproblem 2
r + -3 = -8.94427191 Simplifying r + -3 = -8.94427191 Reorder the terms: -3 + r = -8.94427191 Solving -3 + r = -8.94427191 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + r = -8.94427191 + 3 Combine like terms: -3 + 3 = 0 0 + r = -8.94427191 + 3 r = -8.94427191 + 3 Combine like terms: -8.94427191 + 3 = -5.94427191 r = -5.94427191 Simplifying r = -5.94427191Solution
The solution to the problem is based on the solutions from the subproblems. r = {11.94427191, -5.94427191}
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