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Simplifying -18r6 + -21r5 + -24r4 = 0 Reorder the terms: -24r4 + -21r5 + -18r6 = 0 Solving -24r4 + -21r5 + -18r6 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '-3r4'. -3r4(8 + 7r + 6r2) = 0 Ignore the factor -3.Subproblem 1
Set the factor 'r4' equal to zero and attempt to solve: Simplifying r4 = 0 Solving r4 = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(8 + 7r + 6r2)' equal to zero and attempt to solve: Simplifying 8 + 7r + 6r2 = 0 Solving 8 + 7r + 6r2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.333333333 + 1.166666667r + r2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 1.166666667r + -1.333333333 + r2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 1.166666667r + r2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 1.166666667r + r2 = 0 + -1.333333333 1.166666667r + r2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 1.166666667r + r2 = -1.333333333 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 = -1.333333333 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667r + r2 = -1.333333333 + 0.3402777780 Combine like terms: -1.333333333 + 0.3402777780 = -0.993055555 0.3402777780 + 1.166666667r + r2 = -0.993055555 Factor a perfect square on the left side: (r + 0.5833333335)(r + 0.5833333335) = -0.993055555 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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