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Simplifying 5rp4 + -5rk4 = 0 Reorder the terms: -5k4r + 5p4r = 0 Solving -5k4r + 5p4r = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-5p4r' to each side of the equation. -5k4r + 5p4r + -5p4r = 0 + -5p4r Combine like terms: 5p4r + -5p4r = 0 -5k4r + 0 = 0 + -5p4r -5k4r = 0 + -5p4r Remove the zero: -5k4r = -5p4r Divide each side by '-5r'. k4 = p4 Simplifying k4 = p4 Combine like terms: p4 + -1p4 = 0 k4 + -1p4 = 0 Factor a difference between two squares. (k2 + p2)(k2 + -1p2) = 0 Factor a difference between two squares. (k2 + p2)((k + p)(k + -1p)) = 0Subproblem 1
Set the factor '(k2 + p2)' equal to zero and attempt to solve: Simplifying k2 + p2 = 0 Solving k2 + p2 = 0 Move all terms containing k to the left, all other terms to the right. Add '-1p2' to each side of the equation. k2 + p2 + -1p2 = 0 + -1p2 Combine like terms: p2 + -1p2 = 0 k2 + 0 = 0 + -1p2 k2 = 0 + -1p2 Remove the zero: k2 = -1p2 Simplifying k2 = -1p2 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 '(k + p)' equal to zero and attempt to solve: Simplifying k + p = 0 Solving k + p = 0 Move all terms containing k to the left, all other terms to the right. Add '-1p' to each side of the equation. k + p + -1p = 0 + -1p Combine like terms: p + -1p = 0 k + 0 = 0 + -1p k = 0 + -1p Remove the zero: k = -1p Simplifying k = -1pSubproblem 3
Set the factor '(k + -1p)' equal to zero and attempt to solve: Simplifying k + -1p = 0 Solving k + -1p = 0 Move all terms containing k to the left, all other terms to the right. Add 'p' to each side of the equation. k + -1p + p = 0 + p Combine like terms: -1p + p = 0 k + 0 = 0 + p k = 0 + p Remove the zero: k = p Simplifying k = pSolution
k = {-1p, p}
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