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Simplifying 60x2 + 35xy + 5y2 = 0 Reorder the terms: 35xy + 60x2 + 5y2 = 0 Solving 35xy + 60x2 + 5y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(7xy + 12x2 + y2) = 0 Factor a trinomial. 5((4x + y)(3x + y)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(4x + y)' equal to zero and attempt to solve: Simplifying 4x + y = 0 Solving 4x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 4x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 4x + 0 = 0 + -1y 4x = 0 + -1y Remove the zero: 4x = -1y Divide each side by '4'. x = -0.25y Simplifying x = -0.25ySubproblem 2
Set the factor '(3x + y)' equal to zero and attempt to solve: Simplifying 3x + y = 0 Solving 3x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 3x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 3x + 0 = 0 + -1y 3x = 0 + -1y Remove the zero: 3x = -1y Divide each side by '3'. x = -0.3333333333y Simplifying x = -0.3333333333ySolution
x = {-0.25y, -0.3333333333y}
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