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Simplifying x4 + -9(x2)(y2) + 18y4 = 0 Multiply x2 * y2 x4 + -9x2y2 + 18y4 = 0 Reorder the terms: -9x2y2 + x4 + 18y4 = 0 Solving -9x2y2 + x4 + 18y4 = 0 Solving for variable 'x'. Factor a trinomial. (x2 + -6y2)(x2 + -3y2) = 0Subproblem 1
Set the factor '(x2 + -6y2)' equal to zero and attempt to solve: Simplifying x2 + -6y2 = 0 Solving x2 + -6y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '6y2' to each side of the equation. x2 + -6y2 + 6y2 = 0 + 6y2 Combine like terms: -6y2 + 6y2 = 0 x2 + 0 = 0 + 6y2 x2 = 0 + 6y2 Remove the zero: x2 = 6y2 Simplifying x2 = 6y2 Take the square root of each side: x = {-2.449489743y, 2.449489743y}Subproblem 2
Set the factor '(x2 + -3y2)' equal to zero and attempt to solve: Simplifying x2 + -3y2 = 0 Solving x2 + -3y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '3y2' to each side of the equation. x2 + -3y2 + 3y2 = 0 + 3y2 Combine like terms: -3y2 + 3y2 = 0 x2 + 0 = 0 + 3y2 x2 = 0 + 3y2 Remove the zero: x2 = 3y2 Simplifying x2 = 3y2 Take the square root of each side: x = {-1.732050808y, 1.732050808y}Solution
x = {-2.449489743y, 2.449489743y, -1.732050808y, 1.732050808y}
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