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Simplifying (r + -4)(r + 10) = -29 Reorder the terms: (-4 + r)(r + 10) = -29 Reorder the terms: (-4 + r)(10 + r) = -29 Multiply (-4 + r) * (10 + r) (-4(10 + r) + r(10 + r)) = -29 ((10 * -4 + r * -4) + r(10 + r)) = -29 ((-40 + -4r) + r(10 + r)) = -29 (-40 + -4r + (10 * r + r * r)) = -29 (-40 + -4r + (10r + r2)) = -29 Combine like terms: -4r + 10r = 6r (-40 + 6r + r2) = -29 Solving -40 + 6r + r2 = -29 Solving for variable 'r'. Reorder the terms: -40 + 29 + 6r + r2 = -29 + 29 Combine like terms: -40 + 29 = -11 -11 + 6r + r2 = -29 + 29 Combine like terms: -29 + 29 = 0 -11 + 6r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 6r + 11 + r2 = 0 + 11 Reorder the terms: -11 + 11 + 6r + r2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 6r + r2 = 0 + 11 6r + r2 = 0 + 11 Combine like terms: 0 + 11 = 11 6r + r2 = 11 The r term is 6r. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6r + 9 + r2 = 11 + 9 Reorder the terms: 9 + 6r + r2 = 11 + 9 Combine like terms: 11 + 9 = 20 9 + 6r + r2 = 20 Factor a perfect square on the left side: (r + 3)(r + 3) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (r + 3) equal to 4.472135955 and -4.472135955.Subproblem 1
r + 3 = 4.472135955 Simplifying r + 3 = 4.472135955 Reorder the terms: 3 + r = 4.472135955 Solving 3 + r = 4.472135955 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + r = 4.472135955 + -3 Combine like terms: 3 + -3 = 0 0 + r = 4.472135955 + -3 r = 4.472135955 + -3 Combine like terms: 4.472135955 + -3 = 1.472135955 r = 1.472135955 Simplifying r = 1.472135955Subproblem 2
r + 3 = -4.472135955 Simplifying r + 3 = -4.472135955 Reorder the terms: 3 + r = -4.472135955 Solving 3 + r = -4.472135955 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + r = -4.472135955 + -3 Combine like terms: 3 + -3 = 0 0 + r = -4.472135955 + -3 r = -4.472135955 + -3 Combine like terms: -4.472135955 + -3 = -7.472135955 r = -7.472135955 Simplifying r = -7.472135955Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.472135955, -7.472135955}
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