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Simplifying 18x2 + 40xy + 22y2 = 0 Reorder the terms: 40xy + 18x2 + 22y2 = 0 Solving 40xy + 18x2 + 22y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(20xy + 9x2 + 11y2) = 0 Factor a trinomial. 2((x + y)(9x + 11y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(x + y)' equal to zero and attempt to solve: Simplifying x + y = 0 Solving x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 x + 0 = 0 + -1y x = 0 + -1y Remove the zero: x = -1y Simplifying x = -1ySubproblem 2
Set the factor '(9x + 11y)' equal to zero and attempt to solve: Simplifying 9x + 11y = 0 Solving 9x + 11y = 0 Move all terms containing x to the left, all other terms to the right. Add '-11y' to each side of the equation. 9x + 11y + -11y = 0 + -11y Combine like terms: 11y + -11y = 0 9x + 0 = 0 + -11y 9x = 0 + -11y Remove the zero: 9x = -11y Divide each side by '9'. x = -1.222222222y Simplifying x = -1.222222222ySolution
x = {-1y, -1.222222222y}
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