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Simplifying y4 + -12y2x2 + 36x4 = 0 Reorder the terms: -12x2y2 + 36x4 + y4 = 0 Solving -12x2y2 + 36x4 + y4 = 0 Solving for variable 'x'. Factor a trinomial. (6x2 + -1y2)(6x2 + -1y2) = 0Subproblem 1
Set the factor '(6x2 + -1y2)' equal to zero and attempt to solve: Simplifying 6x2 + -1y2 = 0 Solving 6x2 + -1y2 = 0 Move all terms containing x to the left, all other terms to the right. Add 'y2' to each side of the equation. 6x2 + -1y2 + y2 = 0 + y2 Combine like terms: -1y2 + y2 = 0 6x2 + 0 = 0 + y2 6x2 = 0 + y2 Remove the zero: 6x2 = y2 Divide each side by '6'. x2 = 0.1666666667y2 Simplifying x2 = 0.1666666667y2 Take the square root of each side: x = {-0.408248291y, 0.408248291y}Subproblem 2
Set the factor '(6x2 + -1y2)' equal to zero and attempt to solve: Simplifying 6x2 + -1y2 = 0 Solving 6x2 + -1y2 = 0 Move all terms containing x to the left, all other terms to the right. Add 'y2' to each side of the equation. 6x2 + -1y2 + y2 = 0 + y2 Combine like terms: -1y2 + y2 = 0 6x2 + 0 = 0 + y2 6x2 = 0 + y2 Remove the zero: 6x2 = y2 Divide each side by '6'. x2 = 0.1666666667y2 Simplifying x2 = 0.1666666667y2 Take the square root of each side: x = {-0.408248291y, 0.408248291y}Solution
x = {-0.408248291y, 0.408248291y, -0.408248291y, 0.408248291y}
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