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Simplifying 24r2 + -48r + -245 = 0 Reorder the terms: -245 + -48r + 24r2 = 0 Solving -245 + -48r + 24r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -10.20833333 + -2r + r2 = 0 Move the constant term to the right: Add '10.20833333' to each side of the equation. -10.20833333 + -2r + 10.20833333 + r2 = 0 + 10.20833333 Reorder the terms: -10.20833333 + 10.20833333 + -2r + r2 = 0 + 10.20833333 Combine like terms: -10.20833333 + 10.20833333 = 0.00000000 0.00000000 + -2r + r2 = 0 + 10.20833333 -2r + r2 = 0 + 10.20833333 Combine like terms: 0 + 10.20833333 = 10.20833333 -2r + r2 = 10.20833333 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 = 10.20833333 + 1 Reorder the terms: 1 + -2r + r2 = 10.20833333 + 1 Combine like terms: 10.20833333 + 1 = 11.20833333 1 + -2r + r2 = 11.20833333 Factor a perfect square on the left side: (r + -1)(r + -1) = 11.20833333 Calculate the square root of the right side: 3.347884904 Break this problem into two subproblems by setting (r + -1) equal to 3.347884904 and -3.347884904.Subproblem 1
r + -1 = 3.347884904 Simplifying r + -1 = 3.347884904 Reorder the terms: -1 + r = 3.347884904 Solving -1 + r = 3.347884904 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 = 3.347884904 + 1 Combine like terms: -1 + 1 = 0 0 + r = 3.347884904 + 1 r = 3.347884904 + 1 Combine like terms: 3.347884904 + 1 = 4.347884904 r = 4.347884904 Simplifying r = 4.347884904Subproblem 2
r + -1 = -3.347884904 Simplifying r + -1 = -3.347884904 Reorder the terms: -1 + r = -3.347884904 Solving -1 + r = -3.347884904 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 = -3.347884904 + 1 Combine like terms: -1 + 1 = 0 0 + r = -3.347884904 + 1 r = -3.347884904 + 1 Combine like terms: -3.347884904 + 1 = -2.347884904 r = -2.347884904 Simplifying r = -2.347884904Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.347884904, -2.347884904}
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