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Simplifying 0 = 2x2 + 50y2 + -20xy Reorder the terms: 0 = -20xy + 2x2 + 50y2 Solving 0 = -20xy + 2x2 + 50y2 Solving for variable 'x'. Remove the zero: 20xy + -2x2 + -50y2 = -20xy + 2x2 + 50y2 + 20xy + -2x2 + -50y2 Reorder the terms: 20xy + -2x2 + -50y2 = -20xy + 20xy + 2x2 + -2x2 + 50y2 + -50y2 Combine like terms: -20xy + 20xy = 0 20xy + -2x2 + -50y2 = 0 + 2x2 + -2x2 + 50y2 + -50y2 20xy + -2x2 + -50y2 = 2x2 + -2x2 + 50y2 + -50y2 Combine like terms: 2x2 + -2x2 = 0 20xy + -2x2 + -50y2 = 0 + 50y2 + -50y2 20xy + -2x2 + -50y2 = 50y2 + -50y2 Combine like terms: 50y2 + -50y2 = 0 20xy + -2x2 + -50y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(10xy + -1x2 + -25y2) = 0 Factor a trinomial. 2((-1x + 5y)(x + -5y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1x + 5y)' equal to zero and attempt to solve: Simplifying -1x + 5y = 0 Solving -1x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. -1x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 -1x + 0 = 0 + -5y -1x = 0 + -5y Remove the zero: -1x = -5y Divide each side by '-1'. x = 5y Simplifying x = 5ySubproblem 2
Set the factor '(x + -5y)' equal to zero and attempt to solve: Simplifying x + -5y = 0 Solving x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 x + 0 = 0 + 5y x = 0 + 5y Remove the zero: x = 5y Simplifying x = 5ySolution
x = {5y, 5y}
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