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Simplifying 4x4 + -12x2y2 + 9y4 = 0 Reorder the terms: -12x2y2 + 4x4 + 9y4 = 0 Solving -12x2y2 + 4x4 + 9y4 = 0 Solving for variable 'x'. Factor a trinomial. (2x2 + -3y2)(2x2 + -3y2) = 0Subproblem 1
Set the factor '(2x2 + -3y2)' equal to zero and attempt to solve: Simplifying 2x2 + -3y2 = 0 Solving 2x2 + -3y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '3y2' to each side of the equation. 2x2 + -3y2 + 3y2 = 0 + 3y2 Combine like terms: -3y2 + 3y2 = 0 2x2 + 0 = 0 + 3y2 2x2 = 0 + 3y2 Remove the zero: 2x2 = 3y2 Divide each side by '2'. x2 = 1.5y2 Simplifying x2 = 1.5y2 Take the square root of each side: x = {-1.224744871y, 1.224744871y}Subproblem 2
Set the factor '(2x2 + -3y2)' equal to zero and attempt to solve: Simplifying 2x2 + -3y2 = 0 Solving 2x2 + -3y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '3y2' to each side of the equation. 2x2 + -3y2 + 3y2 = 0 + 3y2 Combine like terms: -3y2 + 3y2 = 0 2x2 + 0 = 0 + 3y2 2x2 = 0 + 3y2 Remove the zero: 2x2 = 3y2 Divide each side by '2'. x2 = 1.5y2 Simplifying x2 = 1.5y2 Take the square root of each side: x = {-1.224744871y, 1.224744871y}Solution
x = {-1.224744871y, 1.224744871y, -1.224744871y, 1.224744871y}
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