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Simplifying (r + -4)(r + 8) = 39 Reorder the terms: (-4 + r)(r + 8) = 39 Reorder the terms: (-4 + r)(8 + r) = 39 Multiply (-4 + r) * (8 + r) (-4(8 + r) + r(8 + r)) = 39 ((8 * -4 + r * -4) + r(8 + r)) = 39 ((-32 + -4r) + r(8 + r)) = 39 (-32 + -4r + (8 * r + r * r)) = 39 (-32 + -4r + (8r + r2)) = 39 Combine like terms: -4r + 8r = 4r (-32 + 4r + r2) = 39 Solving -32 + 4r + r2 = 39 Solving for variable 'r'. Reorder the terms: -32 + -39 + 4r + r2 = 39 + -39 Combine like terms: -32 + -39 = -71 -71 + 4r + r2 = 39 + -39 Combine like terms: 39 + -39 = 0 -71 + 4r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '71' to each side of the equation. -71 + 4r + 71 + r2 = 0 + 71 Reorder the terms: -71 + 71 + 4r + r2 = 0 + 71 Combine like terms: -71 + 71 = 0 0 + 4r + r2 = 0 + 71 4r + r2 = 0 + 71 Combine like terms: 0 + 71 = 71 4r + r2 = 71 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 = 71 + 4 Reorder the terms: 4 + 4r + r2 = 71 + 4 Combine like terms: 71 + 4 = 75 4 + 4r + r2 = 75 Factor a perfect square on the left side: (r + 2)(r + 2) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (r + 2) equal to 8.660254038 and -8.660254038.Subproblem 1
r + 2 = 8.660254038 Simplifying r + 2 = 8.660254038 Reorder the terms: 2 + r = 8.660254038 Solving 2 + r = 8.660254038 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 = 8.660254038 + -2 Combine like terms: 2 + -2 = 0 0 + r = 8.660254038 + -2 r = 8.660254038 + -2 Combine like terms: 8.660254038 + -2 = 6.660254038 r = 6.660254038 Simplifying r = 6.660254038Subproblem 2
r + 2 = -8.660254038 Simplifying r + 2 = -8.660254038 Reorder the terms: 2 + r = -8.660254038 Solving 2 + r = -8.660254038 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 = -8.660254038 + -2 Combine like terms: 2 + -2 = 0 0 + r = -8.660254038 + -2 r = -8.660254038 + -2 Combine like terms: -8.660254038 + -2 = -10.660254038 r = -10.660254038 Simplifying r = -10.660254038Solution
The solution to the problem is based on the solutions from the subproblems. r = {6.660254038, -10.660254038}
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