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Simplifying 4x2 + -14xy + 10y2 = 0 Reorder the terms: -14xy + 4x2 + 10y2 = 0 Solving -14xy + 4x2 + 10y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7xy + 2x2 + 5y2) = 0 Factor a trinomial. 2((2x + -5y)(x + -1y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2x + -5y)' equal to zero and attempt to solve: Simplifying 2x + -5y = 0 Solving 2x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. 2x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 2x + 0 = 0 + 5y 2x = 0 + 5y Remove the zero: 2x = 5y Divide each side by '2'. x = 2.5y Simplifying x = 2.5ySubproblem 2
Set the factor '(x + -1y)' equal to zero and attempt to solve: Simplifying x + -1y = 0 Solving x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. x + -1y + y = 0 + y Combine like terms: -1y + y = 0 x + 0 = 0 + y x = 0 + y Remove the zero: x = y Simplifying x = ySolution
x = {2.5y, y}
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