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Simplifying 24x2 + 26xy + 6y2 = 0 Reorder the terms: 26xy + 24x2 + 6y2 = 0 Solving 26xy + 24x2 + 6y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(13xy + 12x2 + 3y2) = 0 Factor a trinomial. 2((3x + y)(4x + 3y)) = 0 Ignore the factor 2.Subproblem 1
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 = -0.3333333333ySubproblem 2
Set the factor '(4x + 3y)' equal to zero and attempt to solve: Simplifying 4x + 3y = 0 Solving 4x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. 4x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 4x + 0 = 0 + -3y 4x = 0 + -3y Remove the zero: 4x = -3y Divide each side by '4'. x = -0.75y Simplifying x = -0.75ySolution
x = {-0.3333333333y, -0.75y}
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