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Simplifying (r + -3)(r + 13) = -16 Reorder the terms: (-3 + r)(r + 13) = -16 Reorder the terms: (-3 + r)(13 + r) = -16 Multiply (-3 + r) * (13 + r) (-3(13 + r) + r(13 + r)) = -16 ((13 * -3 + r * -3) + r(13 + r)) = -16 ((-39 + -3r) + r(13 + r)) = -16 (-39 + -3r + (13 * r + r * r)) = -16 (-39 + -3r + (13r + r2)) = -16 Combine like terms: -3r + 13r = 10r (-39 + 10r + r2) = -16 Solving -39 + 10r + r2 = -16 Solving for variable 'r'. Reorder the terms: -39 + 16 + 10r + r2 = -16 + 16 Combine like terms: -39 + 16 = -23 -23 + 10r + r2 = -16 + 16 Combine like terms: -16 + 16 = 0 -23 + 10r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + 10r + 23 + r2 = 0 + 23 Reorder the terms: -23 + 23 + 10r + r2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 10r + r2 = 0 + 23 10r + r2 = 0 + 23 Combine like terms: 0 + 23 = 23 10r + r2 = 23 The r term is 10r. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10r + 25 + r2 = 23 + 25 Reorder the terms: 25 + 10r + r2 = 23 + 25 Combine like terms: 23 + 25 = 48 25 + 10r + r2 = 48 Factor a perfect square on the left side: (r + 5)(r + 5) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (r + 5) equal to 6.92820323 and -6.92820323.Subproblem 1
r + 5 = 6.92820323 Simplifying r + 5 = 6.92820323 Reorder the terms: 5 + r = 6.92820323 Solving 5 + r = 6.92820323 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = 6.92820323 + -5 Combine like terms: 5 + -5 = 0 0 + r = 6.92820323 + -5 r = 6.92820323 + -5 Combine like terms: 6.92820323 + -5 = 1.92820323 r = 1.92820323 Simplifying r = 1.92820323Subproblem 2
r + 5 = -6.92820323 Simplifying r + 5 = -6.92820323 Reorder the terms: 5 + r = -6.92820323 Solving 5 + r = -6.92820323 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = -6.92820323 + -5 Combine like terms: 5 + -5 = 0 0 + r = -6.92820323 + -5 r = -6.92820323 + -5 Combine like terms: -6.92820323 + -5 = -11.92820323 r = -11.92820323 Simplifying r = -11.92820323Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.92820323, -11.92820323}
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