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Simplifying r2 + -4r + -9 = 7 Reorder the terms: -9 + -4r + r2 = 7 Solving -9 + -4r + r2 = 7 Solving for variable 'r'. Reorder the terms: -9 + -7 + -4r + r2 = 7 + -7 Combine like terms: -9 + -7 = -16 -16 + -4r + r2 = 7 + -7 Combine like terms: 7 + -7 = 0 -16 + -4r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -4r + 16 + r2 = 0 + 16 Reorder the terms: -16 + 16 + -4r + r2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -4r + r2 = 0 + 16 -4r + r2 = 0 + 16 Combine like terms: 0 + 16 = 16 -4r + r2 = 16 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 = 16 + 4 Reorder the terms: 4 + -4r + r2 = 16 + 4 Combine like terms: 16 + 4 = 20 4 + -4r + r2 = 20 Factor a perfect square on the left side: (r + -2)(r + -2) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (r + -2) equal to 4.472135955 and -4.472135955.Subproblem 1
r + -2 = 4.472135955 Simplifying r + -2 = 4.472135955 Reorder the terms: -2 + r = 4.472135955 Solving -2 + r = 4.472135955 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 = 4.472135955 + 2 Combine like terms: -2 + 2 = 0 0 + r = 4.472135955 + 2 r = 4.472135955 + 2 Combine like terms: 4.472135955 + 2 = 6.472135955 r = 6.472135955 Simplifying r = 6.472135955Subproblem 2
r + -2 = -4.472135955 Simplifying r + -2 = -4.472135955 Reorder the terms: -2 + r = -4.472135955 Solving -2 + r = -4.472135955 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 = -4.472135955 + 2 Combine like terms: -2 + 2 = 0 0 + r = -4.472135955 + 2 r = -4.472135955 + 2 Combine like terms: -4.472135955 + 2 = -2.472135955 r = -2.472135955 Simplifying r = -2.472135955Solution
The solution to the problem is based on the solutions from the subproblems. r = {6.472135955, -2.472135955}
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