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Simplifying r2 + -13 = 8r Reorder the terms: -13 + r2 = 8r Solving -13 + r2 = 8r Solving for variable 'r'. Reorder the terms: -13 + -8r + r2 = 8r + -8r Combine like terms: 8r + -8r = 0 -13 + -8r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -8r + 13 + r2 = 0 + 13 Reorder the terms: -13 + 13 + -8r + r2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -8r + r2 = 0 + 13 -8r + r2 = 0 + 13 Combine like terms: 0 + 13 = 13 -8r + r2 = 13 The r term is -8r. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8r + 16 + r2 = 13 + 16 Reorder the terms: 16 + -8r + r2 = 13 + 16 Combine like terms: 13 + 16 = 29 16 + -8r + r2 = 29 Factor a perfect square on the left side: (r + -4)(r + -4) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (r + -4) equal to 5.385164807 and -5.385164807.Subproblem 1
r + -4 = 5.385164807 Simplifying r + -4 = 5.385164807 Reorder the terms: -4 + r = 5.385164807 Solving -4 + r = 5.385164807 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + r = 5.385164807 + 4 Combine like terms: -4 + 4 = 0 0 + r = 5.385164807 + 4 r = 5.385164807 + 4 Combine like terms: 5.385164807 + 4 = 9.385164807 r = 9.385164807 Simplifying r = 9.385164807Subproblem 2
r + -4 = -5.385164807 Simplifying r + -4 = -5.385164807 Reorder the terms: -4 + r = -5.385164807 Solving -4 + r = -5.385164807 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + r = -5.385164807 + 4 Combine like terms: -4 + 4 = 0 0 + r = -5.385164807 + 4 r = -5.385164807 + 4 Combine like terms: -5.385164807 + 4 = -1.385164807 r = -1.385164807 Simplifying r = -1.385164807Solution
The solution to the problem is based on the solutions from the subproblems. r = {9.385164807, -1.385164807}
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