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Simplifying r2 + -4r + -8 = 0 Reorder the terms: -8 + -4r + r2 = 0 Solving -8 + -4r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -4r + 8 + r2 = 0 + 8 Reorder the terms: -8 + 8 + -4r + r2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -4r + r2 = 0 + 8 -4r + r2 = 0 + 8 Combine like terms: 0 + 8 = 8 -4r + r2 = 8 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 = 8 + 4 Reorder the terms: 4 + -4r + r2 = 8 + 4 Combine like terms: 8 + 4 = 12 4 + -4r + r2 = 12 Factor a perfect square on the left side: (r + -2)(r + -2) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (r + -2) equal to 3.464101615 and -3.464101615.Subproblem 1
r + -2 = 3.464101615 Simplifying r + -2 = 3.464101615 Reorder the terms: -2 + r = 3.464101615 Solving -2 + r = 3.464101615 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 = 3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + r = 3.464101615 + 2 r = 3.464101615 + 2 Combine like terms: 3.464101615 + 2 = 5.464101615 r = 5.464101615 Simplifying r = 5.464101615Subproblem 2
r + -2 = -3.464101615 Simplifying r + -2 = -3.464101615 Reorder the terms: -2 + r = -3.464101615 Solving -2 + r = -3.464101615 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 = -3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + r = -3.464101615 + 2 r = -3.464101615 + 2 Combine like terms: -3.464101615 + 2 = -1.464101615 r = -1.464101615 Simplifying r = -1.464101615Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.464101615, -1.464101615}
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