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Simplifying -14x2 + 22xy + 12y2 = 0 Reorder the terms: 22xy + -14x2 + 12y2 = 0 Solving 22xy + -14x2 + 12y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(11xy + -7x2 + 6y2) = 0 Factor a trinomial. 2((-7x + -3y)(x + -2y)) = 0 Ignore the factor 2.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 '(x + -2y)' equal to zero and attempt to solve: Simplifying x + -2y = 0 Solving x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 x + 0 = 0 + 2y x = 0 + 2y Remove the zero: x = 2y Simplifying x = 2ySolution
x = {-0.4285714286y, 2y}
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