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Simplifying r2 + 4r + -130 = 0 Reorder the terms: -130 + 4r + r2 = 0 Solving -130 + 4r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '130' to each side of the equation. -130 + 4r + 130 + r2 = 0 + 130 Reorder the terms: -130 + 130 + 4r + r2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + 4r + r2 = 0 + 130 4r + r2 = 0 + 130 Combine like terms: 0 + 130 = 130 4r + r2 = 130 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 = 130 + 4 Reorder the terms: 4 + 4r + r2 = 130 + 4 Combine like terms: 130 + 4 = 134 4 + 4r + r2 = 134 Factor a perfect square on the left side: (r + 2)(r + 2) = 134 Calculate the square root of the right side: 11.575836903 Break this problem into two subproblems by setting (r + 2) equal to 11.575836903 and -11.575836903.Subproblem 1
r + 2 = 11.575836903 Simplifying r + 2 = 11.575836903 Reorder the terms: 2 + r = 11.575836903 Solving 2 + r = 11.575836903 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 = 11.575836903 + -2 Combine like terms: 2 + -2 = 0 0 + r = 11.575836903 + -2 r = 11.575836903 + -2 Combine like terms: 11.575836903 + -2 = 9.575836903 r = 9.575836903 Simplifying r = 9.575836903Subproblem 2
r + 2 = -11.575836903 Simplifying r + 2 = -11.575836903 Reorder the terms: 2 + r = -11.575836903 Solving 2 + r = -11.575836903 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 = -11.575836903 + -2 Combine like terms: 2 + -2 = 0 0 + r = -11.575836903 + -2 r = -11.575836903 + -2 Combine like terms: -11.575836903 + -2 = -13.575836903 r = -13.575836903 Simplifying r = -13.575836903Solution
The solution to the problem is based on the solutions from the subproblems. r = {9.575836903, -13.575836903}
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