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Simplifying 25x4 + -30x2y2 + 9y4 = 0 Reorder the terms: -30x2y2 + 25x4 + 9y4 = 0 Solving -30x2y2 + 25x4 + 9y4 = 0 Solving for variable 'x'. Factor a trinomial. (5x2 + -3y2)(5x2 + -3y2) = 0Subproblem 1
Set the factor '(5x2 + -3y2)' equal to zero and attempt to solve: Simplifying 5x2 + -3y2 = 0 Solving 5x2 + -3y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '3y2' to each side of the equation. 5x2 + -3y2 + 3y2 = 0 + 3y2 Combine like terms: -3y2 + 3y2 = 0 5x2 + 0 = 0 + 3y2 5x2 = 0 + 3y2 Remove the zero: 5x2 = 3y2 Divide each side by '5'. x2 = 0.6y2 Simplifying x2 = 0.6y2 Take the square root of each side: x = {-0.774596669y, 0.774596669y}Subproblem 2
Set the factor '(5x2 + -3y2)' equal to zero and attempt to solve: Simplifying 5x2 + -3y2 = 0 Solving 5x2 + -3y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '3y2' to each side of the equation. 5x2 + -3y2 + 3y2 = 0 + 3y2 Combine like terms: -3y2 + 3y2 = 0 5x2 + 0 = 0 + 3y2 5x2 = 0 + 3y2 Remove the zero: 5x2 = 3y2 Divide each side by '5'. x2 = 0.6y2 Simplifying x2 = 0.6y2 Take the square root of each side: x = {-0.774596669y, 0.774596669y}Solution
x = {-0.774596669y, 0.774596669y, -0.774596669y, 0.774596669y}
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