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Simplifying 10x2 + -13xy + 4y2 = 0 Reorder the terms: -13xy + 10x2 + 4y2 = 0 Solving -13xy + 10x2 + 4y2 = 0 Solving for variable 'x'. Factor a trinomial. (5x + -4y)(2x + -1y) = 0Subproblem 1
Set the factor '(5x + -4y)' equal to zero and attempt to solve: Simplifying 5x + -4y = 0 Solving 5x + -4y = 0 Move all terms containing x to the left, all other terms to the right. Add '4y' to each side of the equation. 5x + -4y + 4y = 0 + 4y Combine like terms: -4y + 4y = 0 5x + 0 = 0 + 4y 5x = 0 + 4y Remove the zero: 5x = 4y Divide each side by '5'. x = 0.8y Simplifying x = 0.8ySubproblem 2
Set the factor '(2x + -1y)' equal to zero and attempt to solve: Simplifying 2x + -1y = 0 Solving 2x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 2x + -1y + y = 0 + y Combine like terms: -1y + y = 0 2x + 0 = 0 + y 2x = 0 + y Remove the zero: 2x = y Divide each side by '2'. x = 0.5y Simplifying x = 0.5ySolution
x = {0.8y, 0.5y}
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