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Simplifying s4 + -1r4 = 0 Reorder the terms: -1r4 + s4 = 0 Solving -1r4 + s4 = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1s4' to each side of the equation. -1r4 + s4 + -1s4 = 0 + -1s4 Combine like terms: s4 + -1s4 = 0 -1r4 + 0 = 0 + -1s4 -1r4 = 0 + -1s4 Remove the zero: -1r4 = -1s4 Divide each side by '-1'. r4 = s4 Simplifying r4 = s4 Combine like terms: s4 + -1s4 = 0 r4 + -1s4 = 0 Factor a difference between two squares. (r2 + s2)(r2 + -1s2) = 0 Factor a difference between two squares. (r2 + s2)((r + s)(r + -1s)) = 0Subproblem 1
Set the factor '(r2 + s2)' equal to zero and attempt to solve: Simplifying r2 + s2 = 0 Solving r2 + s2 = 0 Move all terms containing r to the left, all other terms to the right. Add '-1s2' to each side of the equation. r2 + s2 + -1s2 = 0 + -1s2 Combine like terms: s2 + -1s2 = 0 r2 + 0 = 0 + -1s2 r2 = 0 + -1s2 Remove the zero: r2 = -1s2 Simplifying r2 = -1s2 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 '(r + s)' equal to zero and attempt to solve: Simplifying r + s = 0 Solving r + s = 0 Move all terms containing r to the left, all other terms to the right. Add '-1s' to each side of the equation. r + s + -1s = 0 + -1s Combine like terms: s + -1s = 0 r + 0 = 0 + -1s r = 0 + -1s Remove the zero: r = -1s Simplifying r = -1sSubproblem 3
Set the factor '(r + -1s)' equal to zero and attempt to solve: Simplifying r + -1s = 0 Solving r + -1s = 0 Move all terms containing r to the left, all other terms to the right. Add 's' to each side of the equation. r + -1s + s = 0 + s Combine like terms: -1s + s = 0 r + 0 = 0 + s r = 0 + s Remove the zero: r = s Simplifying r = sSolution
r = {-1s, s}
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