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Simplifying 3r3 + -18r2 + -16r = 0 Reorder the terms: -16r + -18r2 + 3r3 = 0 Solving -16r + -18r2 + 3r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r'. r(-16 + -18r + 3r2) = 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 '(-16 + -18r + 3r2)' equal to zero and attempt to solve: Simplifying -16 + -18r + 3r2 = 0 Solving -16 + -18r + 3r2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.333333333 + -6r + r2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + -6r + 5.333333333 + r2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + -6r + r2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + -6r + r2 = 0 + 5.333333333 -6r + r2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 -6r + r2 = 5.333333333 The r term is -6r. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6r + 9 + r2 = 5.333333333 + 9 Reorder the terms: 9 + -6r + r2 = 5.333333333 + 9 Combine like terms: 5.333333333 + 9 = 14.333333333 9 + -6r + r2 = 14.333333333 Factor a perfect square on the left side: (r + -3)(r + -3) = 14.333333333 Calculate the square root of the right side: 3.785938897 Break this problem into two subproblems by setting (r + -3) equal to 3.785938897 and -3.785938897.Subproblem 1
r + -3 = 3.785938897 Simplifying r + -3 = 3.785938897 Reorder the terms: -3 + r = 3.785938897 Solving -3 + r = 3.785938897 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + r = 3.785938897 + 3 Combine like terms: -3 + 3 = 0 0 + r = 3.785938897 + 3 r = 3.785938897 + 3 Combine like terms: 3.785938897 + 3 = 6.785938897 r = 6.785938897 Simplifying r = 6.785938897Subproblem 2
r + -3 = -3.785938897 Simplifying r + -3 = -3.785938897 Reorder the terms: -3 + r = -3.785938897 Solving -3 + r = -3.785938897 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + r = -3.785938897 + 3 Combine like terms: -3 + 3 = 0 0 + r = -3.785938897 + 3 r = -3.785938897 + 3 Combine like terms: -3.785938897 + 3 = -0.785938897 r = -0.785938897 Simplifying r = -0.785938897Solution
The solution to the problem is based on the solutions from the subproblems. r = {6.785938897, -0.785938897}Solution
r = {0, 6.785938897, -0.785938897}
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