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Simplifying (5x2 + 2xy + -4y2) + -1(-5xy + -6y2) = 0 Reorder the terms: (2xy + 5x2 + -4y2) + -1(-5xy + -6y2) = 0 Remove parenthesis around (2xy + 5x2 + -4y2) 2xy + 5x2 + -4y2 + -1(-5xy + -6y2) = 0 2xy + 5x2 + -4y2 + (-5xy * -1 + -6y2 * -1) = 0 2xy + 5x2 + -4y2 + (5xy + 6y2) = 0 Reorder the terms: 2xy + 5xy + 5x2 + -4y2 + 6y2 = 0 Combine like terms: 2xy + 5xy = 7xy 7xy + 5x2 + -4y2 + 6y2 = 0 Combine like terms: -4y2 + 6y2 = 2y2 7xy + 5x2 + 2y2 = 0 Solving 7xy + 5x2 + 2y2 = 0 Solving for variable 'x'. Factor a trinomial. (5x + 2y)(x + y) = 0Subproblem 1
Set the factor '(5x + 2y)' equal to zero and attempt to solve: Simplifying 5x + 2y = 0 Solving 5x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. 5x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 5x + 0 = 0 + -2y 5x = 0 + -2y Remove the zero: 5x = -2y Divide each side by '5'. x = -0.4y Simplifying x = -0.4ySubproblem 2
Set the factor '(x + y)' equal to zero and attempt to solve: Simplifying x + y = 0 Solving x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 x + 0 = 0 + -1y x = 0 + -1y Remove the zero: x = -1y Simplifying x = -1ySolution
x = {-0.4y, -1y}
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