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Simplifying -40x2 + 4xy + 84y2 = 0 Reorder the terms: 4xy + -40x2 + 84y2 = 0 Solving 4xy + -40x2 + 84y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(xy + -10x2 + 21y2) = 0 Factor a trinomial. 4((-5x + -7y)(2x + -3y)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5x + -7y)' equal to zero and attempt to solve: Simplifying -5x + -7y = 0 Solving -5x + -7y = 0 Move all terms containing x to the left, all other terms to the right. Add '7y' to each side of the equation. -5x + -7y + 7y = 0 + 7y Combine like terms: -7y + 7y = 0 -5x + 0 = 0 + 7y -5x = 0 + 7y Remove the zero: -5x = 7y Divide each side by '-5'. x = -1.4y Simplifying x = -1.4ySubproblem 2
Set the factor '(2x + -3y)' equal to zero and attempt to solve: Simplifying 2x + -3y = 0 Solving 2x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. 2x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 2x + 0 = 0 + 3y 2x = 0 + 3y Remove the zero: 2x = 3y Divide each side by '2'. x = 1.5y Simplifying x = 1.5ySolution
x = {-1.4y, 1.5y}
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