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Simplifying 5.5r2 + -96r + -2662 = 0 Reorder the terms: -2662 + -96r + 5.5r2 = 0 Solving -2662 + -96r + 5.5r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 5.5 the coefficient of the squared term: Divide each side by '5.5'. -484 + -17.45454545r + r2 = 0 Move the constant term to the right: Add '484' to each side of the equation. -484 + -17.45454545r + 484 + r2 = 0 + 484 Reorder the terms: -484 + 484 + -17.45454545r + r2 = 0 + 484 Combine like terms: -484 + 484 = 0 0 + -17.45454545r + r2 = 0 + 484 -17.45454545r + r2 = 0 + 484 Combine like terms: 0 + 484 = 484 -17.45454545r + r2 = 484 The r term is -17.45454545r. Take half its coefficient (-8.727272725). Square it (76.16528922) and add it to both sides. Add '76.16528922' to each side of the equation. -17.45454545r + 76.16528922 + r2 = 484 + 76.16528922 Reorder the terms: 76.16528922 + -17.45454545r + r2 = 484 + 76.16528922 Combine like terms: 484 + 76.16528922 = 560.16528922 76.16528922 + -17.45454545r + r2 = 560.16528922 Factor a perfect square on the left side: (r + -8.727272725)(r + -8.727272725) = 560.16528922 Calculate the square root of the right side: 23.667811247 Break this problem into two subproblems by setting (r + -8.727272725) equal to 23.667811247 and -23.667811247.Subproblem 1
r + -8.727272725 = 23.667811247 Simplifying r + -8.727272725 = 23.667811247 Reorder the terms: -8.727272725 + r = 23.667811247 Solving -8.727272725 + r = 23.667811247 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '8.727272725' to each side of the equation. -8.727272725 + 8.727272725 + r = 23.667811247 + 8.727272725 Combine like terms: -8.727272725 + 8.727272725 = 0.000000000 0.000000000 + r = 23.667811247 + 8.727272725 r = 23.667811247 + 8.727272725 Combine like terms: 23.667811247 + 8.727272725 = 32.395083972 r = 32.395083972 Simplifying r = 32.395083972Subproblem 2
r + -8.727272725 = -23.667811247 Simplifying r + -8.727272725 = -23.667811247 Reorder the terms: -8.727272725 + r = -23.667811247 Solving -8.727272725 + r = -23.667811247 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '8.727272725' to each side of the equation. -8.727272725 + 8.727272725 + r = -23.667811247 + 8.727272725 Combine like terms: -8.727272725 + 8.727272725 = 0.000000000 0.000000000 + r = -23.667811247 + 8.727272725 r = -23.667811247 + 8.727272725 Combine like terms: -23.667811247 + 8.727272725 = -14.940538522 r = -14.940538522 Simplifying r = -14.940538522Solution
The solution to the problem is based on the solutions from the subproblems. r = {32.395083972, -14.940538522}
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