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Simplifying 2r2 + -4r + -35 = 0 Reorder the terms: -35 + -4r + 2r2 = 0 Solving -35 + -4r + 2r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -17.5 + -2r + r2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + -2r + 17.5 + r2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + -2r + r2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + -2r + r2 = 0 + 17.5 -2r + r2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 -2r + r2 = 17.5 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 = 17.5 + 1 Reorder the terms: 1 + -2r + r2 = 17.5 + 1 Combine like terms: 17.5 + 1 = 18.5 1 + -2r + r2 = 18.5 Factor a perfect square on the left side: (r + -1)(r + -1) = 18.5 Calculate the square root of the right side: 4.301162634 Break this problem into two subproblems by setting (r + -1) equal to 4.301162634 and -4.301162634.Subproblem 1
r + -1 = 4.301162634 Simplifying r + -1 = 4.301162634 Reorder the terms: -1 + r = 4.301162634 Solving -1 + r = 4.301162634 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 = 4.301162634 + 1 Combine like terms: -1 + 1 = 0 0 + r = 4.301162634 + 1 r = 4.301162634 + 1 Combine like terms: 4.301162634 + 1 = 5.301162634 r = 5.301162634 Simplifying r = 5.301162634Subproblem 2
r + -1 = -4.301162634 Simplifying r + -1 = -4.301162634 Reorder the terms: -1 + r = -4.301162634 Solving -1 + r = -4.301162634 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 = -4.301162634 + 1 Combine like terms: -1 + 1 = 0 0 + r = -4.301162634 + 1 r = -4.301162634 + 1 Combine like terms: -4.301162634 + 1 = -3.301162634 r = -3.301162634 Simplifying r = -3.301162634Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.301162634, -3.301162634}
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