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Simplifying (r + -2)(r + 16) = -6 Reorder the terms: (-2 + r)(r + 16) = -6 Reorder the terms: (-2 + r)(16 + r) = -6 Multiply (-2 + r) * (16 + r) (-2(16 + r) + r(16 + r)) = -6 ((16 * -2 + r * -2) + r(16 + r)) = -6 ((-32 + -2r) + r(16 + r)) = -6 (-32 + -2r + (16 * r + r * r)) = -6 (-32 + -2r + (16r + r2)) = -6 Combine like terms: -2r + 16r = 14r (-32 + 14r + r2) = -6 Solving -32 + 14r + r2 = -6 Solving for variable 'r'. Reorder the terms: -32 + 6 + 14r + r2 = -6 + 6 Combine like terms: -32 + 6 = -26 -26 + 14r + r2 = -6 + 6 Combine like terms: -6 + 6 = 0 -26 + 14r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + 14r + 26 + r2 = 0 + 26 Reorder the terms: -26 + 26 + 14r + r2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 14r + r2 = 0 + 26 14r + r2 = 0 + 26 Combine like terms: 0 + 26 = 26 14r + r2 = 26 The r term is 14r. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14r + 49 + r2 = 26 + 49 Reorder the terms: 49 + 14r + r2 = 26 + 49 Combine like terms: 26 + 49 = 75 49 + 14r + r2 = 75 Factor a perfect square on the left side: (r + 7)(r + 7) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (r + 7) equal to 8.660254038 and -8.660254038.Subproblem 1
r + 7 = 8.660254038 Simplifying r + 7 = 8.660254038 Reorder the terms: 7 + r = 8.660254038 Solving 7 + r = 8.660254038 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + r = 8.660254038 + -7 Combine like terms: 7 + -7 = 0 0 + r = 8.660254038 + -7 r = 8.660254038 + -7 Combine like terms: 8.660254038 + -7 = 1.660254038 r = 1.660254038 Simplifying r = 1.660254038Subproblem 2
r + 7 = -8.660254038 Simplifying r + 7 = -8.660254038 Reorder the terms: 7 + r = -8.660254038 Solving 7 + r = -8.660254038 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + r = -8.660254038 + -7 Combine like terms: 7 + -7 = 0 0 + r = -8.660254038 + -7 r = -8.660254038 + -7 Combine like terms: -8.660254038 + -7 = -15.660254038 r = -15.660254038 Simplifying r = -15.660254038Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.660254038, -15.660254038}
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