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Simplifying 100xy + -50y2 + 50x2 + -25xy = 0 Reorder the terms: 100xy + -25xy + 50x2 + -50y2 = 0 Combine like terms: 100xy + -25xy = 75xy 75xy + 50x2 + -50y2 = 0 Solving 75xy + 50x2 + -50y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '25'. 25(3xy + 2x2 + -2y2) = 0 Factor a trinomial. 25((2x + -1y)(x + 2y)) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(2x + -1y)' equal to zero and attempt to solve: Simplifying 2x + -1y = 0 Solving 2x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 2x + -1y + y = 0 + y Combine like terms: -1y + y = 0 2x + 0 = 0 + y 2x = 0 + y Remove the zero: 2x = y Divide each side by '2'. x = 0.5y Simplifying x = 0.5ySubproblem 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 = {0.5y, -2y}
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