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Simplifying r2 + -2r + -79 = 0 Reorder the terms: -79 + -2r + r2 = 0 Solving -79 + -2r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '79' to each side of the equation. -79 + -2r + 79 + r2 = 0 + 79 Reorder the terms: -79 + 79 + -2r + r2 = 0 + 79 Combine like terms: -79 + 79 = 0 0 + -2r + r2 = 0 + 79 -2r + r2 = 0 + 79 Combine like terms: 0 + 79 = 79 -2r + r2 = 79 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 = 79 + 1 Reorder the terms: 1 + -2r + r2 = 79 + 1 Combine like terms: 79 + 1 = 80 1 + -2r + r2 = 80 Factor a perfect square on the left side: (r + -1)(r + -1) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (r + -1) equal to 8.94427191 and -8.94427191.Subproblem 1
r + -1 = 8.94427191 Simplifying r + -1 = 8.94427191 Reorder the terms: -1 + r = 8.94427191 Solving -1 + r = 8.94427191 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 = 8.94427191 + 1 Combine like terms: -1 + 1 = 0 0 + r = 8.94427191 + 1 r = 8.94427191 + 1 Combine like terms: 8.94427191 + 1 = 9.94427191 r = 9.94427191 Simplifying r = 9.94427191Subproblem 2
r + -1 = -8.94427191 Simplifying r + -1 = -8.94427191 Reorder the terms: -1 + r = -8.94427191 Solving -1 + r = -8.94427191 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 = -8.94427191 + 1 Combine like terms: -1 + 1 = 0 0 + r = -8.94427191 + 1 r = -8.94427191 + 1 Combine like terms: -8.94427191 + 1 = -7.94427191 r = -7.94427191 Simplifying r = -7.94427191Solution
The solution to the problem is based on the solutions from the subproblems. r = {9.94427191, -7.94427191}
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