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Simplifying 0 = 4x2 + -19xy + -5y2 Reorder the terms: 0 = -19xy + 4x2 + -5y2 Solving 0 = -19xy + 4x2 + -5y2 Solving for variable 'x'. Remove the zero: 19xy + -4x2 + 5y2 = -19xy + 4x2 + -5y2 + 19xy + -4x2 + 5y2 Reorder the terms: 19xy + -4x2 + 5y2 = -19xy + 19xy + 4x2 + -4x2 + -5y2 + 5y2 Combine like terms: -19xy + 19xy = 0 19xy + -4x2 + 5y2 = 0 + 4x2 + -4x2 + -5y2 + 5y2 19xy + -4x2 + 5y2 = 4x2 + -4x2 + -5y2 + 5y2 Combine like terms: 4x2 + -4x2 = 0 19xy + -4x2 + 5y2 = 0 + -5y2 + 5y2 19xy + -4x2 + 5y2 = -5y2 + 5y2 Combine like terms: -5y2 + 5y2 = 0 19xy + -4x2 + 5y2 = 0 Factor a trinomial. (-4x + -1y)(x + -5y) = 0Subproblem 1
Set the factor '(-4x + -1y)' equal to zero and attempt to solve: Simplifying -4x + -1y = 0 Solving -4x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. -4x + -1y + y = 0 + y Combine like terms: -1y + y = 0 -4x + 0 = 0 + y -4x = 0 + y Remove the zero: -4x = y Divide each side by '-4'. x = -0.25y Simplifying x = -0.25ySubproblem 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 = {-0.25y, 5y}
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