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Simplifying 75x2 + -30xy + 3y2 = 0 Reorder the terms: -30xy + 75x2 + 3y2 = 0 Solving -30xy + 75x2 + 3y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-10xy + 25x2 + y2) = 0 Factor a trinomial. 3((5x + -1y)(5x + -1y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5x + -1y)' equal to zero and attempt to solve: Simplifying 5x + -1y = 0 Solving 5x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 5x + -1y + y = 0 + y Combine like terms: -1y + y = 0 5x + 0 = 0 + y 5x = 0 + y Remove the zero: 5x = y Divide each side by '5'. x = 0.2y Simplifying x = 0.2ySubproblem 2
Set the factor '(5x + -1y)' equal to zero and attempt to solve: Simplifying 5x + -1y = 0 Solving 5x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 5x + -1y + y = 0 + y Combine like terms: -1y + y = 0 5x + 0 = 0 + y 5x = 0 + y Remove the zero: 5x = y Divide each side by '5'. x = 0.2y Simplifying x = 0.2ySolution
x = {0.2y, 0.2y}
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