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Simplifying (3x + -1y)(3x + -1y) = 0 Multiply (3x + -1y) * (3x + -1y) (3x * (3x + -1y) + -1y * (3x + -1y)) = 0 ((3x * 3x + -1y * 3x) + -1y * (3x + -1y)) = 0 Reorder the terms: ((-3xy + 9x2) + -1y * (3x + -1y)) = 0 ((-3xy + 9x2) + -1y * (3x + -1y)) = 0 (-3xy + 9x2 + (3x * -1y + -1y * -1y)) = 0 (-3xy + 9x2 + (-3xy + 1y2)) = 0 Reorder the terms: (-3xy + -3xy + 9x2 + 1y2) = 0 Combine like terms: -3xy + -3xy = -6xy (-6xy + 9x2 + 1y2) = 0 Solving -6xy + 9x2 + 1y2 = 0 Solving for variable 'x'. Factor a trinomial. (3x + -1y)(3x + -1y) = 0Subproblem 1
Set the factor '(3x + -1y)' equal to zero and attempt to solve: Simplifying 3x + -1y = 0 Solving 3x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 3x + -1y + y = 0 + y Combine like terms: -1y + y = 0 3x + 0 = 0 + y 3x = 0 + y Remove the zero: 3x = y Divide each side by '3'. x = 0.3333333333y Simplifying x = 0.3333333333ySubproblem 2
Set the factor '(3x + -1y)' equal to zero and attempt to solve: Simplifying 3x + -1y = 0 Solving 3x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 3x + -1y + y = 0 + y Combine like terms: -1y + y = 0 3x + 0 = 0 + y 3x = 0 + y Remove the zero: 3x = y Divide each side by '3'. x = 0.3333333333y Simplifying x = 0.3333333333ySolution
x = {0.3333333333y, 0.3333333333y}
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