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Simplifying 0 = 64x2 + 112xy + 49y2 Reorder the terms: 0 = 112xy + 64x2 + 49y2 Solving 0 = 112xy + 64x2 + 49y2 Solving for variable 'x'. Remove the zero: -112xy + -64x2 + -49y2 = 112xy + 64x2 + 49y2 + -112xy + -64x2 + -49y2 Reorder the terms: -112xy + -64x2 + -49y2 = 112xy + -112xy + 64x2 + -64x2 + 49y2 + -49y2 Combine like terms: 112xy + -112xy = 0 -112xy + -64x2 + -49y2 = 0 + 64x2 + -64x2 + 49y2 + -49y2 -112xy + -64x2 + -49y2 = 64x2 + -64x2 + 49y2 + -49y2 Combine like terms: 64x2 + -64x2 = 0 -112xy + -64x2 + -49y2 = 0 + 49y2 + -49y2 -112xy + -64x2 + -49y2 = 49y2 + -49y2 Combine like terms: 49y2 + -49y2 = 0 -112xy + -64x2 + -49y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(112xy + 64x2 + 49y2) = 0 Factor a trinomial. -1((8x + 7y)(8x + 7y)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8x + 7y)' equal to zero and attempt to solve: Simplifying 8x + 7y = 0 Solving 8x + 7y = 0 Move all terms containing x to the left, all other terms to the right. Add '-7y' to each side of the equation. 8x + 7y + -7y = 0 + -7y Combine like terms: 7y + -7y = 0 8x + 0 = 0 + -7y 8x = 0 + -7y Remove the zero: 8x = -7y Divide each side by '8'. x = -0.875y Simplifying x = -0.875ySubproblem 2
Set the factor '(8x + 7y)' equal to zero and attempt to solve: Simplifying 8x + 7y = 0 Solving 8x + 7y = 0 Move all terms containing x to the left, all other terms to the right. Add '-7y' to each side of the equation. 8x + 7y + -7y = 0 + -7y Combine like terms: 7y + -7y = 0 8x + 0 = 0 + -7y 8x = 0 + -7y Remove the zero: 8x = -7y Divide each side by '8'. x = -0.875y Simplifying x = -0.875ySolution
x = {-0.875y, -0.875y}
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