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Simplifying 4x2 + 54xy + -90y2 = 0 Reorder the terms: 54xy + 4x2 + -90y2 = 0 Solving 54xy + 4x2 + -90y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(27xy + 2x2 + -45y2) = 0 Factor a trinomial. 2((2x + -3y)(x + 15y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2x + -3y)' equal to zero and attempt to solve: Simplifying 2x + -3y = 0 Solving 2x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. 2x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 2x + 0 = 0 + 3y 2x = 0 + 3y Remove the zero: 2x = 3y Divide each side by '2'. x = 1.5y Simplifying x = 1.5ySubproblem 2
Set the factor '(x + 15y)' equal to zero and attempt to solve: Simplifying x + 15y = 0 Solving x + 15y = 0 Move all terms containing x to the left, all other terms to the right. Add '-15y' to each side of the equation. x + 15y + -15y = 0 + -15y Combine like terms: 15y + -15y = 0 x + 0 = 0 + -15y x = 0 + -15y Remove the zero: x = -15y Simplifying x = -15ySolution
x = {1.5y, -15y}
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