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Simplifying -42x2 + 306xy + -84y2 = 0 Reorder the terms: 306xy + -42x2 + -84y2 = 0 Solving 306xy + -42x2 + -84y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(51xy + -7x2 + -14y2) = 0 Factor a trinomial. 6((-7x + 2y)(x + -7y)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-7x + 2y)' equal to zero and attempt to solve: Simplifying -7x + 2y = 0 Solving -7x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. -7x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 -7x + 0 = 0 + -2y -7x = 0 + -2y Remove the zero: -7x = -2y Divide each side by '-7'. x = 0.2857142857y Simplifying x = 0.2857142857ySubproblem 2
Set the factor '(x + -7y)' equal to zero and attempt to solve: Simplifying x + -7y = 0 Solving x + -7y = 0 Move all terms containing x to the left, all other terms to the right. Add '7y' to each side of the equation. x + -7y + 7y = 0 + 7y Combine like terms: -7y + 7y = 0 x + 0 = 0 + 7y x = 0 + 7y Remove the zero: x = 7y Simplifying x = 7ySolution
x = {0.2857142857y, 7y}
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