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Simplifying r2 + 4r + -42 = 0 Reorder the terms: -42 + 4r + r2 = 0 Solving -42 + 4r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + 4r + 42 + r2 = 0 + 42 Reorder the terms: -42 + 42 + 4r + r2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 4r + r2 = 0 + 42 4r + r2 = 0 + 42 Combine like terms: 0 + 42 = 42 4r + r2 = 42 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 = 42 + 4 Reorder the terms: 4 + 4r + r2 = 42 + 4 Combine like terms: 42 + 4 = 46 4 + 4r + r2 = 46 Factor a perfect square on the left side: (r + 2)(r + 2) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (r + 2) equal to 6.782329983 and -6.782329983.Subproblem 1
r + 2 = 6.782329983 Simplifying r + 2 = 6.782329983 Reorder the terms: 2 + r = 6.782329983 Solving 2 + r = 6.782329983 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 = 6.782329983 + -2 Combine like terms: 2 + -2 = 0 0 + r = 6.782329983 + -2 r = 6.782329983 + -2 Combine like terms: 6.782329983 + -2 = 4.782329983 r = 4.782329983 Simplifying r = 4.782329983Subproblem 2
r + 2 = -6.782329983 Simplifying r + 2 = -6.782329983 Reorder the terms: 2 + r = -6.782329983 Solving 2 + r = -6.782329983 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 = -6.782329983 + -2 Combine like terms: 2 + -2 = 0 0 + r = -6.782329983 + -2 r = -6.782329983 + -2 Combine like terms: -6.782329983 + -2 = -8.782329983 r = -8.782329983 Simplifying r = -8.782329983Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.782329983, -8.782329983}
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