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Simplifying (4x + -1y)(4x + -1y) = 0 Multiply (4x + -1y) * (4x + -1y) (4x * (4x + -1y) + -1y * (4x + -1y)) = 0 ((4x * 4x + -1y * 4x) + -1y * (4x + -1y)) = 0 Reorder the terms: ((-4xy + 16x2) + -1y * (4x + -1y)) = 0 ((-4xy + 16x2) + -1y * (4x + -1y)) = 0 (-4xy + 16x2 + (4x * -1y + -1y * -1y)) = 0 (-4xy + 16x2 + (-4xy + 1y2)) = 0 Reorder the terms: (-4xy + -4xy + 16x2 + 1y2) = 0 Combine like terms: -4xy + -4xy = -8xy (-8xy + 16x2 + 1y2) = 0 Solving -8xy + 16x2 + 1y2 = 0 Solving for variable 'x'. Factor a trinomial. (4x + -1y)(4x + -1y) = 0Subproblem 1
Set the factor '(4x + -1y)' equal to zero and attempt to solve: Simplifying 4x + -1y = 0 Solving 4x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 4x + -1y + y = 0 + y Combine like terms: -1y + y = 0 4x + 0 = 0 + y 4x = 0 + y Remove the zero: 4x = y Divide each side by '4'. x = 0.25y Simplifying x = 0.25ySubproblem 2
Set the factor '(4x + -1y)' equal to zero and attempt to solve: Simplifying 4x + -1y = 0 Solving 4x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 4x + -1y + y = 0 + y Combine like terms: -1y + y = 0 4x + 0 = 0 + y 4x = 0 + y Remove the zero: 4x = y Divide each side by '4'. x = 0.25y Simplifying x = 0.25ySolution
x = {0.25y, 0.25y}
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