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Simplifying 45x2 + 113xy + 12y2 = 0 Reorder the terms: 113xy + 45x2 + 12y2 = 0 Solving 113xy + 45x2 + 12y2 = 0 Solving for variable 'x'. Factor a trinomial. (9x + y)(5x + 12y) = 0Subproblem 1
Set the factor '(9x + y)' equal to zero and attempt to solve: Simplifying 9x + y = 0 Solving 9x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 9x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 9x + 0 = 0 + -1y 9x = 0 + -1y Remove the zero: 9x = -1y Divide each side by '9'. x = -0.1111111111y Simplifying x = -0.1111111111ySubproblem 2
Set the factor '(5x + 12y)' equal to zero and attempt to solve: Simplifying 5x + 12y = 0 Solving 5x + 12y = 0 Move all terms containing x to the left, all other terms to the right. Add '-12y' to each side of the equation. 5x + 12y + -12y = 0 + -12y Combine like terms: 12y + -12y = 0 5x + 0 = 0 + -12y 5x = 0 + -12y Remove the zero: 5x = -12y Divide each side by '5'. x = -2.4y Simplifying x = -2.4ySolution
x = {-0.1111111111y, -2.4y}
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