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Simplifying r2 + -6r + -83 = -10 Reorder the terms: -83 + -6r + r2 = -10 Solving -83 + -6r + r2 = -10 Solving for variable 'r'. Reorder the terms: -83 + 10 + -6r + r2 = -10 + 10 Combine like terms: -83 + 10 = -73 -73 + -6r + r2 = -10 + 10 Combine like terms: -10 + 10 = 0 -73 + -6r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '73' to each side of the equation. -73 + -6r + 73 + r2 = 0 + 73 Reorder the terms: -73 + 73 + -6r + r2 = 0 + 73 Combine like terms: -73 + 73 = 0 0 + -6r + r2 = 0 + 73 -6r + r2 = 0 + 73 Combine like terms: 0 + 73 = 73 -6r + r2 = 73 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 = 73 + 9 Reorder the terms: 9 + -6r + r2 = 73 + 9 Combine like terms: 73 + 9 = 82 9 + -6r + r2 = 82 Factor a perfect square on the left side: (r + -3)(r + -3) = 82 Calculate the square root of the right side: 9.055385138 Break this problem into two subproblems by setting (r + -3) equal to 9.055385138 and -9.055385138.Subproblem 1
r + -3 = 9.055385138 Simplifying r + -3 = 9.055385138 Reorder the terms: -3 + r = 9.055385138 Solving -3 + r = 9.055385138 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 = 9.055385138 + 3 Combine like terms: -3 + 3 = 0 0 + r = 9.055385138 + 3 r = 9.055385138 + 3 Combine like terms: 9.055385138 + 3 = 12.055385138 r = 12.055385138 Simplifying r = 12.055385138Subproblem 2
r + -3 = -9.055385138 Simplifying r + -3 = -9.055385138 Reorder the terms: -3 + r = -9.055385138 Solving -3 + r = -9.055385138 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 = -9.055385138 + 3 Combine like terms: -3 + 3 = 0 0 + r = -9.055385138 + 3 r = -9.055385138 + 3 Combine like terms: -9.055385138 + 3 = -6.055385138 r = -6.055385138 Simplifying r = -6.055385138Solution
The solution to the problem is based on the solutions from the subproblems. r = {12.055385138, -6.055385138}
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