R^6-r^2=0

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Solution for R^6-r^2=0 equation:


Simplifying
R6 + -1r2 = 0

Solving
R6 + -1r2 = 0

Solving for variable 'R'.

Move all terms containing R to the left, all other terms to the right.

Add 'r2' to each side of the equation.
R6 + -1r2 + r2 = 0 + r2

Combine like terms: -1r2 + r2 = 0
R6 + 0 = 0 + r2
R6 = 0 + r2
Remove the zero:
R6 = r2

Simplifying
R6 = r2

Combine like terms: r2 + -1r2 = 0
R6 + -1r2 = 0

Factor a difference between two squares.
(R3 + r)(R3 + -1r) = 0

Subproblem 1

Set the factor '(R3 + r)' equal to zero and attempt to solve: Simplifying R3 + r = 0 Solving R3 + r = 0 Move all terms containing R to the left, all other terms to the right. Add '-1r' to each side of the equation. R3 + r + -1r = 0 + -1r Combine like terms: r + -1r = 0 R3 + 0 = 0 + -1r R3 = 0 + -1r Remove the zero: R3 = -1r Simplifying R3 = -1r 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 '(R3 + -1r)' equal to zero and attempt to solve: Simplifying R3 + -1r = 0 Solving R3 + -1r = 0 Move all terms containing R to the left, all other terms to the right. Add 'r' to each side of the equation. R3 + -1r + r = 0 + r Combine like terms: -1r + r = 0 R3 + 0 = 0 + r R3 = 0 + r Remove the zero: R3 = r Simplifying R3 = r 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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