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Simplifying y4 + x4 = y4 + p4 Reorder the terms: x4 + y4 = y4 + p4 Reorder the terms: x4 + y4 = p4 + y4 Add '-1y4' to each side of the equation. x4 + y4 + -1y4 = p4 + y4 + -1y4 Combine like terms: y4 + -1y4 = 0 x4 + 0 = p4 + y4 + -1y4 x4 = p4 + y4 + -1y4 Combine like terms: y4 + -1y4 = 0 x4 = p4 + 0 x4 = p4 Solving x4 = p4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Simplifying x4 = p4 Reorder the terms: -1p4 + x4 = p4 + -1p4 Combine like terms: p4 + -1p4 = 0 -1p4 + x4 = 0 Factor a difference between two squares. (p2 + x2)(-1p2 + x2) = 0 Factor a difference between two squares. (p2 + x2)((p + x)(-1p + x)) = 0Subproblem 1
Set the factor '(p2 + x2)' equal to zero and attempt to solve: Simplifying p2 + x2 = 0 Solving p2 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1p2' to each side of the equation. p2 + -1p2 + x2 = 0 + -1p2 Combine like terms: p2 + -1p2 = 0 0 + x2 = 0 + -1p2 x2 = 0 + -1p2 Remove the zero: x2 = -1p2 Simplifying x2 = -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 '(p + x)' equal to zero and attempt to solve: Simplifying p + x = 0 Solving p + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1p' to each side of the equation. p + -1p + x = 0 + -1p Combine like terms: p + -1p = 0 0 + x = 0 + -1p x = 0 + -1p Remove the zero: x = -1p Simplifying x = -1pSubproblem 3
Set the factor '(-1p + x)' equal to zero and attempt to solve: Simplifying -1p + x = 0 Solving -1p + x = 0 Move all terms containing x to the left, all other terms to the right. Add 'p' to each side of the equation. -1p + p + x = 0 + p Combine like terms: -1p + p = 0 0 + x = 0 + p x = 0 + p Remove the zero: x = p Simplifying x = pSolution
x = {-1p, p}
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