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Simplifying 16x4 + -24x2y2 + 9y4 = 0 Reorder the terms: -24x2y2 + 16x4 + 9y4 = 0 Solving -24x2y2 + 16x4 + 9y4 = 0 Solving for variable 'x'. Factor a trinomial. (4x2 + -3y2)(4x2 + -3y2) = 0Subproblem 1
Set the factor '(4x2 + -3y2)' equal to zero and attempt to solve: Simplifying 4x2 + -3y2 = 0 Solving 4x2 + -3y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '3y2' to each side of the equation. 4x2 + -3y2 + 3y2 = 0 + 3y2 Combine like terms: -3y2 + 3y2 = 0 4x2 + 0 = 0 + 3y2 4x2 = 0 + 3y2 Remove the zero: 4x2 = 3y2 Divide each side by '4'. x2 = 0.75y2 Simplifying x2 = 0.75y2 Take the square root of each side: x = {-0.866025404y, 0.866025404y}Subproblem 2
Set the factor '(4x2 + -3y2)' equal to zero and attempt to solve: Simplifying 4x2 + -3y2 = 0 Solving 4x2 + -3y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '3y2' to each side of the equation. 4x2 + -3y2 + 3y2 = 0 + 3y2 Combine like terms: -3y2 + 3y2 = 0 4x2 + 0 = 0 + 3y2 4x2 = 0 + 3y2 Remove the zero: 4x2 = 3y2 Divide each side by '4'. x2 = 0.75y2 Simplifying x2 = 0.75y2 Take the square root of each side: x = {-0.866025404y, 0.866025404y}Solution
x = {-0.866025404y, 0.866025404y, -0.866025404y, 0.866025404y}
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