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Simplifying r2 + -1r = 47 Reorder the terms: -1r + r2 = 47 Solving -1r + r2 = 47 Solving for variable 'r'. Reorder the terms: -47 + -1r + r2 = 47 + -47 Combine like terms: 47 + -47 = 0 -47 + -1r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + -1r + 47 + r2 = 0 + 47 Reorder the terms: -47 + 47 + -1r + r2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -1r + r2 = 0 + 47 -1r + r2 = 0 + 47 Combine like terms: 0 + 47 = 47 -1r + r2 = 47 The r term is -1r. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1r + 0.25 + r2 = 47 + 0.25 Reorder the terms: 0.25 + -1r + r2 = 47 + 0.25 Combine like terms: 47 + 0.25 = 47.25 0.25 + -1r + r2 = 47.25 Factor a perfect square on the left side: (r + -0.5)(r + -0.5) = 47.25 Calculate the square root of the right side: 6.873863542 Break this problem into two subproblems by setting (r + -0.5) equal to 6.873863542 and -6.873863542.Subproblem 1
r + -0.5 = 6.873863542 Simplifying r + -0.5 = 6.873863542 Reorder the terms: -0.5 + r = 6.873863542 Solving -0.5 + r = 6.873863542 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + r = 6.873863542 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + r = 6.873863542 + 0.5 r = 6.873863542 + 0.5 Combine like terms: 6.873863542 + 0.5 = 7.373863542 r = 7.373863542 Simplifying r = 7.373863542Subproblem 2
r + -0.5 = -6.873863542 Simplifying r + -0.5 = -6.873863542 Reorder the terms: -0.5 + r = -6.873863542 Solving -0.5 + r = -6.873863542 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + r = -6.873863542 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + r = -6.873863542 + 0.5 r = -6.873863542 + 0.5 Combine like terms: -6.873863542 + 0.5 = -6.373863542 r = -6.373863542 Simplifying r = -6.373863542Solution
The solution to the problem is based on the solutions from the subproblems. r = {7.373863542, -6.373863542}
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