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Simplifying (r + -2)(r + 12) = 26 Reorder the terms: (-2 + r)(r + 12) = 26 Reorder the terms: (-2 + r)(12 + r) = 26 Multiply (-2 + r) * (12 + r) (-2(12 + r) + r(12 + r)) = 26 ((12 * -2 + r * -2) + r(12 + r)) = 26 ((-24 + -2r) + r(12 + r)) = 26 (-24 + -2r + (12 * r + r * r)) = 26 (-24 + -2r + (12r + r2)) = 26 Combine like terms: -2r + 12r = 10r (-24 + 10r + r2) = 26 Solving -24 + 10r + r2 = 26 Solving for variable 'r'. Reorder the terms: -24 + -26 + 10r + r2 = 26 + -26 Combine like terms: -24 + -26 = -50 -50 + 10r + r2 = 26 + -26 Combine like terms: 26 + -26 = 0 -50 + 10r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 10r + 50 + r2 = 0 + 50 Reorder the terms: -50 + 50 + 10r + r2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 10r + r2 = 0 + 50 10r + r2 = 0 + 50 Combine like terms: 0 + 50 = 50 10r + r2 = 50 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 = 50 + 25 Reorder the terms: 25 + 10r + r2 = 50 + 25 Combine like terms: 50 + 25 = 75 25 + 10r + r2 = 75 Factor a perfect square on the left side: (r + 5)(r + 5) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (r + 5) equal to 8.660254038 and -8.660254038.Subproblem 1
r + 5 = 8.660254038 Simplifying r + 5 = 8.660254038 Reorder the terms: 5 + r = 8.660254038 Solving 5 + r = 8.660254038 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 = 8.660254038 + -5 Combine like terms: 5 + -5 = 0 0 + r = 8.660254038 + -5 r = 8.660254038 + -5 Combine like terms: 8.660254038 + -5 = 3.660254038 r = 3.660254038 Simplifying r = 3.660254038Subproblem 2
r + 5 = -8.660254038 Simplifying r + 5 = -8.660254038 Reorder the terms: 5 + r = -8.660254038 Solving 5 + r = -8.660254038 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 = -8.660254038 + -5 Combine like terms: 5 + -5 = 0 0 + r = -8.660254038 + -5 r = -8.660254038 + -5 Combine like terms: -8.660254038 + -5 = -13.660254038 r = -13.660254038 Simplifying r = -13.660254038Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.660254038, -13.660254038}
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