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Simplifying 245x2 + -210xy + 45y2 = 0 Reorder the terms: -210xy + 245x2 + 45y2 = 0 Solving -210xy + 245x2 + 45y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-42xy + 49x2 + 9y2) = 0 Factor a trinomial. 5((7x + -3y)(7x + -3y)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(7x + -3y)' equal to zero and attempt to solve: Simplifying 7x + -3y = 0 Solving 7x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. 7x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 7x + 0 = 0 + 3y 7x = 0 + 3y Remove the zero: 7x = 3y Divide each side by '7'. x = 0.4285714286y Simplifying x = 0.4285714286ySubproblem 2
Set the factor '(7x + -3y)' equal to zero and attempt to solve: Simplifying 7x + -3y = 0 Solving 7x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. 7x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 7x + 0 = 0 + 3y 7x = 0 + 3y Remove the zero: 7x = 3y Divide each side by '7'. x = 0.4285714286y Simplifying x = 0.4285714286ySolution
x = {0.4285714286y, 0.4285714286y}
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