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Simplifying 7x4 + -6x2y2 + -1y4 = 0 Reorder the terms: -6x2y2 + 7x4 + -1y4 = 0 Solving -6x2y2 + 7x4 + -1y4 = 0 Solving for variable 'x'. Factor a trinomial. (x2 + -1y2)(7x2 + y2) = 0 Factor a difference between two squares. ((x + y)(x + -1y))(7x2 + y2) = 0Subproblem 1
Set the factor '(7x2 + y2)' equal to zero and attempt to solve: Simplifying 7x2 + y2 = 0 Solving 7x2 + y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y2' to each side of the equation. 7x2 + y2 + -1y2 = 0 + -1y2 Combine like terms: y2 + -1y2 = 0 7x2 + 0 = 0 + -1y2 7x2 = 0 + -1y2 Remove the zero: 7x2 = -1y2 Divide each side by '7'. x2 = -0.1428571429y2 Simplifying x2 = -0.1428571429y2 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 '(x + y)' equal to zero and attempt to solve: Simplifying x + y = 0 Solving x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 x + 0 = 0 + -1y x = 0 + -1y Remove the zero: x = -1y Simplifying x = -1ySubproblem 3
Set the factor '(x + -1y)' equal to zero and attempt to solve: Simplifying x + -1y = 0 Solving x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. x + -1y + y = 0 + y Combine like terms: -1y + y = 0 x + 0 = 0 + y x = 0 + y Remove the zero: x = y Simplifying x = ySolution
x = {-1y, y}
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