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Simplifying 9r3(8r2 + 6)(8r2 + -6) = 0 Reorder the terms: 9r3(6 + 8r2)(8r2 + -6) = 0 Reorder the terms: 9r3(6 + 8r2)(-6 + 8r2) = 0 Multiply (6 + 8r2) * (-6 + 8r2) 9r3(6(-6 + 8r2) + 8r2 * (-6 + 8r2)) = 0 9r3((-6 * 6 + 8r2 * 6) + 8r2 * (-6 + 8r2)) = 0 9r3((-36 + 48r2) + 8r2 * (-6 + 8r2)) = 0 9r3(-36 + 48r2 + (-6 * 8r2 + 8r2 * 8r2)) = 0 9r3(-36 + 48r2 + (-48r2 + 64r4)) = 0 Combine like terms: 48r2 + -48r2 = 0 9r3(-36 + 0 + 64r4) = 0 9r3(-36 + 64r4) = 0 (-36 * 9r3 + 64r4 * 9r3) = 0 (-324r3 + 576r7) = 0 Solving -324r3 + 576r7 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '36r3'. 36r3(-9 + 16r4) = 0 Factor a difference between two squares. 36r3((3 + 4r2)(-3 + 4r2)) = 0 Ignore the factor 36.Subproblem 1
Set the factor 'r3' equal to zero and attempt to solve: Simplifying r3 = 0 Solving r3 = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r3 = 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 '(3 + 4r2)' equal to zero and attempt to solve: Simplifying 3 + 4r2 = 0 Solving 3 + 4r2 = 0 Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4r2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4r2 = 0 + -3 4r2 = 0 + -3 Combine like terms: 0 + -3 = -3 4r2 = -3 Divide each side by '4'. r2 = -0.75 Simplifying r2 = -0.75 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(-3 + 4r2)' equal to zero and attempt to solve: Simplifying -3 + 4r2 = 0 Solving -3 + 4r2 = 0 Move all terms containing r to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 4r2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4r2 = 0 + 3 4r2 = 0 + 3 Combine like terms: 0 + 3 = 3 4r2 = 3 Divide each side by '4'. r2 = 0.75 Simplifying r2 = 0.75 Take the square root of each side: r = {-0.866025404, 0.866025404}Solution
r = {-0.866025404, 0.866025404}
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