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Simplifying r2 + -2r = 43 Reorder the terms: -2r + r2 = 43 Solving -2r + r2 = 43 Solving for variable 'r'. Reorder the terms: -43 + -2r + r2 = 43 + -43 Combine like terms: 43 + -43 = 0 -43 + -2r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + -2r + 43 + r2 = 0 + 43 Reorder the terms: -43 + 43 + -2r + r2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -2r + r2 = 0 + 43 -2r + r2 = 0 + 43 Combine like terms: 0 + 43 = 43 -2r + r2 = 43 The r term is -2r. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2r + 1 + r2 = 43 + 1 Reorder the terms: 1 + -2r + r2 = 43 + 1 Combine like terms: 43 + 1 = 44 1 + -2r + r2 = 44 Factor a perfect square on the left side: (r + -1)(r + -1) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (r + -1) equal to 6.633249581 and -6.633249581.Subproblem 1
r + -1 = 6.633249581 Simplifying r + -1 = 6.633249581 Reorder the terms: -1 + r = 6.633249581 Solving -1 + r = 6.633249581 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + r = 6.633249581 + 1 Combine like terms: -1 + 1 = 0 0 + r = 6.633249581 + 1 r = 6.633249581 + 1 Combine like terms: 6.633249581 + 1 = 7.633249581 r = 7.633249581 Simplifying r = 7.633249581Subproblem 2
r + -1 = -6.633249581 Simplifying r + -1 = -6.633249581 Reorder the terms: -1 + r = -6.633249581 Solving -1 + r = -6.633249581 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + r = -6.633249581 + 1 Combine like terms: -1 + 1 = 0 0 + r = -6.633249581 + 1 r = -6.633249581 + 1 Combine like terms: -6.633249581 + 1 = -5.633249581 r = -5.633249581 Simplifying r = -5.633249581Solution
The solution to the problem is based on the solutions from the subproblems. r = {7.633249581, -5.633249581}
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