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Simplifying 6r3 + -7r2 + -207r = 0 Reorder the terms: -207r + -7r2 + 6r3 = 0 Solving -207r + -7r2 + 6r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r'. r(-207 + -7r + 6r2) = 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 '(-207 + -7r + 6r2)' equal to zero and attempt to solve: Simplifying -207 + -7r + 6r2 = 0 Solving -207 + -7r + 6r2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -34.5 + -1.166666667r + r2 = 0 Move the constant term to the right: Add '34.5' to each side of the equation. -34.5 + -1.166666667r + 34.5 + r2 = 0 + 34.5 Reorder the terms: -34.5 + 34.5 + -1.166666667r + r2 = 0 + 34.5 Combine like terms: -34.5 + 34.5 = 0.0 0.0 + -1.166666667r + r2 = 0 + 34.5 -1.166666667r + r2 = 0 + 34.5 Combine like terms: 0 + 34.5 = 34.5 -1.166666667r + r2 = 34.5 The r term is -1.166666667r. Take half its coefficient (-0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. -1.166666667r + 0.3402777780 + r2 = 34.5 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667r + r2 = 34.5 + 0.3402777780 Combine like terms: 34.5 + 0.3402777780 = 34.840277778 0.3402777780 + -1.166666667r + r2 = 34.840277778 Factor a perfect square on the left side: (r + -0.5833333335)(r + -0.5833333335) = 34.840277778 Calculate the square root of the right side: 5.902565356 Break this problem into two subproblems by setting (r + -0.5833333335) equal to 5.902565356 and -5.902565356.Subproblem 1
r + -0.5833333335 = 5.902565356 Simplifying r + -0.5833333335 = 5.902565356 Reorder the terms: -0.5833333335 + r = 5.902565356 Solving -0.5833333335 + r = 5.902565356 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + r = 5.902565356 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + r = 5.902565356 + 0.5833333335 r = 5.902565356 + 0.5833333335 Combine like terms: 5.902565356 + 0.5833333335 = 6.4858986895 r = 6.4858986895 Simplifying r = 6.4858986895Subproblem 2
r + -0.5833333335 = -5.902565356 Simplifying r + -0.5833333335 = -5.902565356 Reorder the terms: -0.5833333335 + r = -5.902565356 Solving -0.5833333335 + r = -5.902565356 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + r = -5.902565356 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + r = -5.902565356 + 0.5833333335 r = -5.902565356 + 0.5833333335 Combine like terms: -5.902565356 + 0.5833333335 = -5.3192320225 r = -5.3192320225 Simplifying r = -5.3192320225Solution
The solution to the problem is based on the solutions from the subproblems. r = {6.4858986895, -5.3192320225}Solution
r = {0, 6.4858986895, -5.3192320225}
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