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Simplifying -8x2 + 40xy + 112y2 = 0 Reorder the terms: 40xy + -8x2 + 112y2 = 0 Solving 40xy + -8x2 + 112y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(5xy + -1x2 + 14y2) = 0 Factor a trinomial. 8((-1x + -2y)(x + -7y)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-1x + -2y)' equal to zero and attempt to solve: Simplifying -1x + -2y = 0 Solving -1x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. -1x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 -1x + 0 = 0 + 2y -1x = 0 + 2y Remove the zero: -1x = 2y Divide each side by '-1'. x = -2y Simplifying x = -2ySubproblem 2
Set the factor '(x + -7y)' equal to zero and attempt to solve: Simplifying x + -7y = 0 Solving x + -7y = 0 Move all terms containing x to the left, all other terms to the right. Add '7y' to each side of the equation. x + -7y + 7y = 0 + 7y Combine like terms: -7y + 7y = 0 x + 0 = 0 + 7y x = 0 + 7y Remove the zero: x = 7y Simplifying x = 7ySolution
x = {-2y, 7y}
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