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Simplifying 4x2(y2) + -4xyz + z2 = 0 Multiply x2 * y2 4x2y2 + -4xyz + z2 = 0 Reorder the terms: -4xyz + 4x2y2 + z2 = 0 Solving -4xyz + 4x2y2 + z2 = 0 Solving for variable 'x'. Factor a trinomial. (2xy + -1z)(2xy + -1z) = 0Subproblem 1
Set the factor '(2xy + -1z)' equal to zero and attempt to solve: Simplifying 2xy + -1z = 0 Solving 2xy + -1z = 0 Move all terms containing x to the left, all other terms to the right. Add 'z' to each side of the equation. 2xy + -1z + z = 0 + z Combine like terms: -1z + z = 0 2xy + 0 = 0 + z 2xy = 0 + z Remove the zero: 2xy = z Divide each side by '2y'. x = 0.5y-1z Simplifying x = 0.5y-1zSubproblem 2
Set the factor '(2xy + -1z)' equal to zero and attempt to solve: Simplifying 2xy + -1z = 0 Solving 2xy + -1z = 0 Move all terms containing x to the left, all other terms to the right. Add 'z' to each side of the equation. 2xy + -1z + z = 0 + z Combine like terms: -1z + z = 0 2xy + 0 = 0 + z 2xy = 0 + z Remove the zero: 2xy = z Divide each side by '2y'. x = 0.5y-1z Simplifying x = 0.5y-1zSolution
x = {0.5y-1z, 0.5y-1z}
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