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Simplifying 2r3 + -17r2 + -33r = 0 Reorder the terms: -33r + -17r2 + 2r3 = 0 Solving -33r + -17r2 + 2r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r'. r(-33 + -17r + 2r2) = 0Subproblem 1
Set the factor 'r' equal to zero and attempt to solve: Simplifying r = 0 Solving r = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r = 0Subproblem 2
Set the factor '(-33 + -17r + 2r2)' equal to zero and attempt to solve: Simplifying -33 + -17r + 2r2 = 0 Solving -33 + -17r + 2r2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -16.5 + -8.5r + r2 = 0 Move the constant term to the right: Add '16.5' to each side of the equation. -16.5 + -8.5r + 16.5 + r2 = 0 + 16.5 Reorder the terms: -16.5 + 16.5 + -8.5r + r2 = 0 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + -8.5r + r2 = 0 + 16.5 -8.5r + r2 = 0 + 16.5 Combine like terms: 0 + 16.5 = 16.5 -8.5r + r2 = 16.5 The r term is -8.5r. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5r + 18.0625 + r2 = 16.5 + 18.0625 Reorder the terms: 18.0625 + -8.5r + r2 = 16.5 + 18.0625 Combine like terms: 16.5 + 18.0625 = 34.5625 18.0625 + -8.5r + r2 = 34.5625 Factor a perfect square on the left side: (r + -4.25)(r + -4.25) = 34.5625 Calculate the square root of the right side: 5.878988008 Break this problem into two subproblems by setting (r + -4.25) equal to 5.878988008 and -5.878988008.Subproblem 1
r + -4.25 = 5.878988008 Simplifying r + -4.25 = 5.878988008 Reorder the terms: -4.25 + r = 5.878988008 Solving -4.25 + r = 5.878988008 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + r = 5.878988008 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + r = 5.878988008 + 4.25 r = 5.878988008 + 4.25 Combine like terms: 5.878988008 + 4.25 = 10.128988008 r = 10.128988008 Simplifying r = 10.128988008Subproblem 2
r + -4.25 = -5.878988008 Simplifying r + -4.25 = -5.878988008 Reorder the terms: -4.25 + r = -5.878988008 Solving -4.25 + r = -5.878988008 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + r = -5.878988008 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + r = -5.878988008 + 4.25 r = -5.878988008 + 4.25 Combine like terms: -5.878988008 + 4.25 = -1.628988008 r = -1.628988008 Simplifying r = -1.628988008Solution
The solution to the problem is based on the solutions from the subproblems. r = {10.128988008, -1.628988008}Solution
r = {0, 10.128988008, -1.628988008}
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