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Simplifying -10x2 + -27xy + -5y2 = 0 Reorder the terms: -27xy + -10x2 + -5y2 = 0 Solving -27xy + -10x2 + -5y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(27xy + 10x2 + 5y2) = 0 Factor a trinomial. -1((5x + y)(2x + 5y)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5x + y)' equal to zero and attempt to solve: Simplifying 5x + y = 0 Solving 5x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 5x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 5x + 0 = 0 + -1y 5x = 0 + -1y Remove the zero: 5x = -1y Divide each side by '5'. x = -0.2y Simplifying x = -0.2ySubproblem 2
Set the factor '(2x + 5y)' equal to zero and attempt to solve: Simplifying 2x + 5y = 0 Solving 2x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. 2x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 2x + 0 = 0 + -5y 2x = 0 + -5y Remove the zero: 2x = -5y Divide each side by '2'. x = -2.5y Simplifying x = -2.5ySolution
x = {-0.2y, -2.5y}
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