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Simplifying (4x + -1y)(x + -7y) = 0 Multiply (4x + -1y) * (x + -7y) (4x * (x + -7y) + -1y * (x + -7y)) = 0 ((x * 4x + -7y * 4x) + -1y * (x + -7y)) = 0 Reorder the terms: ((-28xy + 4x2) + -1y * (x + -7y)) = 0 ((-28xy + 4x2) + -1y * (x + -7y)) = 0 (-28xy + 4x2 + (x * -1y + -7y * -1y)) = 0 (-28xy + 4x2 + (-1xy + 7y2)) = 0 Reorder the terms: (-28xy + -1xy + 4x2 + 7y2) = 0 Combine like terms: -28xy + -1xy = -29xy (-29xy + 4x2 + 7y2) = 0 Solving -29xy + 4x2 + 7y2 = 0 Solving for variable 'x'. Factor a trinomial. (x + -7y)(4x + -1y) = 0Subproblem 1
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 = 7ySubproblem 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 = {7y, 0.25y}
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