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Simplifying 16y4 + -24x2y2 + 9x4 = 0 Reorder the terms: -24x2y2 + 9x4 + 16y4 = 0 Solving -24x2y2 + 9x4 + 16y4 = 0 Solving for variable 'x'. Factor a trinomial. (3x2 + -4y2)(3x2 + -4y2) = 0Subproblem 1
Set the factor '(3x2 + -4y2)' equal to zero and attempt to solve: Simplifying 3x2 + -4y2 = 0 Solving 3x2 + -4y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '4y2' to each side of the equation. 3x2 + -4y2 + 4y2 = 0 + 4y2 Combine like terms: -4y2 + 4y2 = 0 3x2 + 0 = 0 + 4y2 3x2 = 0 + 4y2 Remove the zero: 3x2 = 4y2 Divide each side by '3'. x2 = 1.333333333y2 Simplifying x2 = 1.333333333y2 Take the square root of each side: x = {-1.154700538y, 1.154700538y}Subproblem 2
Set the factor '(3x2 + -4y2)' equal to zero and attempt to solve: Simplifying 3x2 + -4y2 = 0 Solving 3x2 + -4y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '4y2' to each side of the equation. 3x2 + -4y2 + 4y2 = 0 + 4y2 Combine like terms: -4y2 + 4y2 = 0 3x2 + 0 = 0 + 4y2 3x2 = 0 + 4y2 Remove the zero: 3x2 = 4y2 Divide each side by '3'. x2 = 1.333333333y2 Simplifying x2 = 1.333333333y2 Take the square root of each side: x = {-1.154700538y, 1.154700538y}Solution
x = {-1.154700538y, 1.154700538y, -1.154700538y, 1.154700538y}
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