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Simplifying r2 + -4r + -1 = 0 Reorder the terms: -1 + -4r + r2 = 0 Solving -1 + -4r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -4r + 1 + r2 = 0 + 1 Reorder the terms: -1 + 1 + -4r + r2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4r + r2 = 0 + 1 -4r + r2 = 0 + 1 Combine like terms: 0 + 1 = 1 -4r + r2 = 1 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 = 1 + 4 Reorder the terms: 4 + -4r + r2 = 1 + 4 Combine like terms: 1 + 4 = 5 4 + -4r + r2 = 5 Factor a perfect square on the left side: (r + -2)(r + -2) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (r + -2) equal to 2.236067978 and -2.236067978.Subproblem 1
r + -2 = 2.236067978 Simplifying r + -2 = 2.236067978 Reorder the terms: -2 + r = 2.236067978 Solving -2 + r = 2.236067978 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 = 2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + r = 2.236067978 + 2 r = 2.236067978 + 2 Combine like terms: 2.236067978 + 2 = 4.236067978 r = 4.236067978 Simplifying r = 4.236067978Subproblem 2
r + -2 = -2.236067978 Simplifying r + -2 = -2.236067978 Reorder the terms: -2 + r = -2.236067978 Solving -2 + r = -2.236067978 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 = -2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + r = -2.236067978 + 2 r = -2.236067978 + 2 Combine like terms: -2.236067978 + 2 = -0.236067978 r = -0.236067978 Simplifying r = -0.236067978Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.236067978, -0.236067978}
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