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Simplifying r2 + -4r + -79 = 0 Reorder the terms: -79 + -4r + r2 = 0 Solving -79 + -4r + 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 + -4r + 79 + r2 = 0 + 79 Reorder the terms: -79 + 79 + -4r + r2 = 0 + 79 Combine like terms: -79 + 79 = 0 0 + -4r + r2 = 0 + 79 -4r + r2 = 0 + 79 Combine like terms: 0 + 79 = 79 -4r + r2 = 79 The r term is -4r. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4r + 4 + r2 = 79 + 4 Reorder the terms: 4 + -4r + r2 = 79 + 4 Combine like terms: 79 + 4 = 83 4 + -4r + r2 = 83 Factor a perfect square on the left side: (r + -2)(r + -2) = 83 Calculate the square root of the right side: 9.110433579 Break this problem into two subproblems by setting (r + -2) equal to 9.110433579 and -9.110433579.Subproblem 1
r + -2 = 9.110433579 Simplifying r + -2 = 9.110433579 Reorder the terms: -2 + r = 9.110433579 Solving -2 + r = 9.110433579 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + r = 9.110433579 + 2 Combine like terms: -2 + 2 = 0 0 + r = 9.110433579 + 2 r = 9.110433579 + 2 Combine like terms: 9.110433579 + 2 = 11.110433579 r = 11.110433579 Simplifying r = 11.110433579Subproblem 2
r + -2 = -9.110433579 Simplifying r + -2 = -9.110433579 Reorder the terms: -2 + r = -9.110433579 Solving -2 + r = -9.110433579 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + r = -9.110433579 + 2 Combine like terms: -2 + 2 = 0 0 + r = -9.110433579 + 2 r = -9.110433579 + 2 Combine like terms: -9.110433579 + 2 = -7.110433579 r = -7.110433579 Simplifying r = -7.110433579Solution
The solution to the problem is based on the solutions from the subproblems. r = {11.110433579, -7.110433579}
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