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Simplifying 40x2 + 116xy + -84y2 = 0 Reorder the terms: 116xy + 40x2 + -84y2 = 0 Solving 116xy + 40x2 + -84y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(29xy + 10x2 + -21y2) = 0 Factor a trinomial. 4((5x + -3y)(2x + 7y)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5x + -3y)' equal to zero and attempt to solve: Simplifying 5x + -3y = 0 Solving 5x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. 5x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 5x + 0 = 0 + 3y 5x = 0 + 3y Remove the zero: 5x = 3y Divide each side by '5'. x = 0.6y Simplifying x = 0.6ySubproblem 2
Set the factor '(2x + 7y)' equal to zero and attempt to solve: Simplifying 2x + 7y = 0 Solving 2x + 7y = 0 Move all terms containing x to the left, all other terms to the right. Add '-7y' to each side of the equation. 2x + 7y + -7y = 0 + -7y Combine like terms: 7y + -7y = 0 2x + 0 = 0 + -7y 2x = 0 + -7y Remove the zero: 2x = -7y Divide each side by '2'. x = -3.5y Simplifying x = -3.5ySolution
x = {0.6y, -3.5y}
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