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Simplifying -4x2 + -1y2 + 4z2 + 8z = 0 Reorder the terms: -4x2 + -1y2 + 8z + 4z2 = 0 Solving -4x2 + -1y2 + 8z + 4z2 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add 'y2' to each side of the equation. -4x2 + -1y2 + 8z + y2 + 4z2 = 0 + y2 Reorder the terms: -4x2 + -1y2 + y2 + 8z + 4z2 = 0 + y2 Combine like terms: -1y2 + y2 = 0 -4x2 + 0 + 8z + 4z2 = 0 + y2 -4x2 + 8z + 4z2 = 0 + y2 Remove the zero: -4x2 + 8z + 4z2 = y2 Add '-8z' to each side of the equation. -4x2 + 8z + -8z + 4z2 = y2 + -8z Combine like terms: 8z + -8z = 0 -4x2 + 0 + 4z2 = y2 + -8z -4x2 + 4z2 = y2 + -8z Add '-4z2' to each side of the equation. -4x2 + 4z2 + -4z2 = y2 + -8z + -4z2 Combine like terms: 4z2 + -4z2 = 0 -4x2 + 0 = y2 + -8z + -4z2 -4x2 = y2 + -8z + -4z2 Divide each side by '-4'. x2 = -0.25y2 + 2z + z2 Simplifying x2 = -0.25y2 + 2z + z2 Reorder the terms: x2 + 0.25y2 + -2z + -1z2 = -0.25y2 + 0.25y2 + 2z + -2z + z2 + -1z2 Combine like terms: -0.25y2 + 0.25y2 = 0.00 x2 + 0.25y2 + -2z + -1z2 = 0.00 + 2z + -2z + z2 + -1z2 x2 + 0.25y2 + -2z + -1z2 = 2z + -2z + z2 + -1z2 Combine like terms: 2z + -2z = 0 x2 + 0.25y2 + -2z + -1z2 = 0 + z2 + -1z2 x2 + 0.25y2 + -2z + -1z2 = z2 + -1z2 Combine like terms: z2 + -1z2 = 0 x2 + 0.25y2 + -2z + -1z2 = 0 The solution to this equation could not be determined.
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