5r^6-45r^2=0

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Solution for 5r^6-45r^2=0 equation:


Simplifying
5r6 + -45r2 = 0

Reorder the terms:
-45r2 + 5r6 = 0

Solving
-45r2 + 5r6 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '5r2'.
5r2(-9 + r4) = 0

Factor a difference between two squares.
5r2((3 + r2)(-3 + r2)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor 'r2' equal to zero and attempt to solve: Simplifying r2 = 0 Solving r2 = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r2 = 0 Take the square root of each side: r = {0}

Subproblem 2

Set the factor '(3 + r2)' equal to zero and attempt to solve: Simplifying 3 + r2 = 0 Solving 3 + r2 = 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 + r2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + r2 = 0 + -3 r2 = 0 + -3 Combine like terms: 0 + -3 = -3 r2 = -3 Simplifying r2 = -3 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 + r2)' equal to zero and attempt to solve: Simplifying -3 + r2 = 0 Solving -3 + r2 = 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 + r2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + r2 = 0 + 3 r2 = 0 + 3 Combine like terms: 0 + 3 = 3 r2 = 3 Simplifying r2 = 3 Take the square root of each side: r = {-1.732050808, 1.732050808}

Solution

r = {0, -1.732050808, 1.732050808}

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