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Simplifying -18x2 + 61xy + 7y2 = 0 Reorder the terms: 61xy + -18x2 + 7y2 = 0 Solving 61xy + -18x2 + 7y2 = 0 Solving for variable 'x'. Factor a trinomial. (-9x + -1y)(2x + -7y) = 0Subproblem 1
Set the factor '(-9x + -1y)' equal to zero and attempt to solve: Simplifying -9x + -1y = 0 Solving -9x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. -9x + -1y + y = 0 + y Combine like terms: -1y + y = 0 -9x + 0 = 0 + y -9x = 0 + y Remove the zero: -9x = y Divide each side by '-9'. x = -0.1111111111y Simplifying x = -0.1111111111ySubproblem 2
Set the factor '(2x + -7y)' equal to zero and attempt to solve: Simplifying 2x + -7y = 0 Solving 2x + -7y = 0 Move all terms containing x to the left, all other terms to the right. Add '7y' to each side of the equation. 2x + -7y + 7y = 0 + 7y Combine like terms: -7y + 7y = 0 2x + 0 = 0 + 7y 2x = 0 + 7y Remove the zero: 2x = 7y Divide each side by '2'. x = 3.5y Simplifying x = 3.5ySolution
x = {-0.1111111111y, 3.5y}
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