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Simplifying 15x2 + -2y2 = 7xy Solving 15x2 + -2y2 = 7xy Solving for variable 'x'. Reorder the terms: -7xy + 15x2 + -2y2 = 7xy + -7xy Combine like terms: 7xy + -7xy = 0 -7xy + 15x2 + -2y2 = 0 Factor a trinomial. (3x + -2y)(5x + y) = 0Subproblem 1
Set the factor '(3x + -2y)' equal to zero and attempt to solve: Simplifying 3x + -2y = 0 Solving 3x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. 3x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 3x + 0 = 0 + 2y 3x = 0 + 2y Remove the zero: 3x = 2y Divide each side by '3'. x = 0.6666666667y Simplifying x = 0.6666666667ySubproblem 2
Set the factor '(5x + y)' equal to zero and attempt to solve: Simplifying 5x + y = 0 Solving 5x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 5x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 5x + 0 = 0 + -1y 5x = 0 + -1y Remove the zero: 5x = -1y Divide each side by '5'. x = -0.2y Simplifying x = -0.2ySolution
x = {0.6666666667y, -0.2y}
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