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Simplifying 0 = x2 + -5xy + -24y2 Reorder the terms: 0 = -5xy + x2 + -24y2 Solving 0 = -5xy + x2 + -24y2 Solving for variable 'x'. Remove the zero: 5xy + -1x2 + 24y2 = -5xy + x2 + -24y2 + 5xy + -1x2 + 24y2 Reorder the terms: 5xy + -1x2 + 24y2 = -5xy + 5xy + x2 + -1x2 + -24y2 + 24y2 Combine like terms: -5xy + 5xy = 0 5xy + -1x2 + 24y2 = 0 + x2 + -1x2 + -24y2 + 24y2 5xy + -1x2 + 24y2 = x2 + -1x2 + -24y2 + 24y2 Combine like terms: x2 + -1x2 = 0 5xy + -1x2 + 24y2 = 0 + -24y2 + 24y2 5xy + -1x2 + 24y2 = -24y2 + 24y2 Combine like terms: -24y2 + 24y2 = 0 5xy + -1x2 + 24y2 = 0 Factor a trinomial. (-1x + -3y)(x + -8y) = 0Subproblem 1
Set the factor '(-1x + -3y)' equal to zero and attempt to solve: Simplifying -1x + -3y = 0 Solving -1x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. -1x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 -1x + 0 = 0 + 3y -1x = 0 + 3y Remove the zero: -1x = 3y Divide each side by '-1'. x = -3y Simplifying x = -3ySubproblem 2
Set the factor '(x + -8y)' equal to zero and attempt to solve: Simplifying x + -8y = 0 Solving x + -8y = 0 Move all terms containing x to the left, all other terms to the right. Add '8y' to each side of the equation. x + -8y + 8y = 0 + 8y Combine like terms: -8y + 8y = 0 x + 0 = 0 + 8y x = 0 + 8y Remove the zero: x = 8y Simplifying x = 8ySolution
x = {-3y, 8y}
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