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Simplifying r2 + 6r + -99 = 0 Reorder the terms: -99 + 6r + r2 = 0 Solving -99 + 6r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + 6r + 99 + r2 = 0 + 99 Reorder the terms: -99 + 99 + 6r + r2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + 6r + r2 = 0 + 99 6r + r2 = 0 + 99 Combine like terms: 0 + 99 = 99 6r + r2 = 99 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 = 99 + 9 Reorder the terms: 9 + 6r + r2 = 99 + 9 Combine like terms: 99 + 9 = 108 9 + 6r + r2 = 108 Factor a perfect square on the left side: (r + 3)(r + 3) = 108 Calculate the square root of the right side: 10.392304845 Break this problem into two subproblems by setting (r + 3) equal to 10.392304845 and -10.392304845.Subproblem 1
r + 3 = 10.392304845 Simplifying r + 3 = 10.392304845 Reorder the terms: 3 + r = 10.392304845 Solving 3 + r = 10.392304845 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 = 10.392304845 + -3 Combine like terms: 3 + -3 = 0 0 + r = 10.392304845 + -3 r = 10.392304845 + -3 Combine like terms: 10.392304845 + -3 = 7.392304845 r = 7.392304845 Simplifying r = 7.392304845Subproblem 2
r + 3 = -10.392304845 Simplifying r + 3 = -10.392304845 Reorder the terms: 3 + r = -10.392304845 Solving 3 + r = -10.392304845 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 = -10.392304845 + -3 Combine like terms: 3 + -3 = 0 0 + r = -10.392304845 + -3 r = -10.392304845 + -3 Combine like terms: -10.392304845 + -3 = -13.392304845 r = -13.392304845 Simplifying r = -13.392304845Solution
The solution to the problem is based on the solutions from the subproblems. r = {7.392304845, -13.392304845}
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