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Simplifying 0 = 42x2 + 11xy + -3y2 Reorder the terms: 0 = 11xy + 42x2 + -3y2 Solving 0 = 11xy + 42x2 + -3y2 Solving for variable 'x'. Remove the zero: -11xy + -42x2 + 3y2 = 11xy + 42x2 + -3y2 + -11xy + -42x2 + 3y2 Reorder the terms: -11xy + -42x2 + 3y2 = 11xy + -11xy + 42x2 + -42x2 + -3y2 + 3y2 Combine like terms: 11xy + -11xy = 0 -11xy + -42x2 + 3y2 = 0 + 42x2 + -42x2 + -3y2 + 3y2 -11xy + -42x2 + 3y2 = 42x2 + -42x2 + -3y2 + 3y2 Combine like terms: 42x2 + -42x2 = 0 -11xy + -42x2 + 3y2 = 0 + -3y2 + 3y2 -11xy + -42x2 + 3y2 = -3y2 + 3y2 Combine like terms: -3y2 + 3y2 = 0 -11xy + -42x2 + 3y2 = 0 Factor a trinomial. (-7x + -3y)(6x + -1y) = 0Subproblem 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 '(6x + -1y)' equal to zero and attempt to solve: Simplifying 6x + -1y = 0 Solving 6x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 6x + -1y + y = 0 + y Combine like terms: -1y + y = 0 6x + 0 = 0 + y 6x = 0 + y Remove the zero: 6x = y Divide each side by '6'. x = 0.1666666667y Simplifying x = 0.1666666667ySolution
x = {-0.4285714286y, 0.1666666667y}
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