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Simplifying (r + 2)(r + 2) = 15 Reorder the terms: (2 + r)(r + 2) = 15 Reorder the terms: (2 + r)(2 + r) = 15 Multiply (2 + r) * (2 + r) (2(2 + r) + r(2 + r)) = 15 ((2 * 2 + r * 2) + r(2 + r)) = 15 ((4 + 2r) + r(2 + r)) = 15 (4 + 2r + (2 * r + r * r)) = 15 (4 + 2r + (2r + r2)) = 15 Combine like terms: 2r + 2r = 4r (4 + 4r + r2) = 15 Solving 4 + 4r + r2 = 15 Solving for variable 'r'. Reorder the terms: 4 + -15 + 4r + r2 = 15 + -15 Combine like terms: 4 + -15 = -11 -11 + 4r + r2 = 15 + -15 Combine like terms: 15 + -15 = 0 -11 + 4r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 4r + 11 + r2 = 0 + 11 Reorder the terms: -11 + 11 + 4r + r2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 4r + r2 = 0 + 11 4r + r2 = 0 + 11 Combine like terms: 0 + 11 = 11 4r + r2 = 11 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 = 11 + 4 Reorder the terms: 4 + 4r + r2 = 11 + 4 Combine like terms: 11 + 4 = 15 4 + 4r + r2 = 15 Factor a perfect square on the left side: (r + 2)(r + 2) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (r + 2) equal to 3.872983346 and -3.872983346.Subproblem 1
r + 2 = 3.872983346 Simplifying r + 2 = 3.872983346 Reorder the terms: 2 + r = 3.872983346 Solving 2 + r = 3.872983346 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 = 3.872983346 + -2 Combine like terms: 2 + -2 = 0 0 + r = 3.872983346 + -2 r = 3.872983346 + -2 Combine like terms: 3.872983346 + -2 = 1.872983346 r = 1.872983346 Simplifying r = 1.872983346Subproblem 2
r + 2 = -3.872983346 Simplifying r + 2 = -3.872983346 Reorder the terms: 2 + r = -3.872983346 Solving 2 + r = -3.872983346 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 = -3.872983346 + -2 Combine like terms: 2 + -2 = 0 0 + r = -3.872983346 + -2 r = -3.872983346 + -2 Combine like terms: -3.872983346 + -2 = -5.872983346 r = -5.872983346 Simplifying r = -5.872983346Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.872983346, -5.872983346}
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