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Simplifying 4x2 + y2 + -2y + 4z2 = 0 Reorder the terms: 4x2 + -2y + y2 + 4z2 = 0 Solving 4x2 + -2y + y2 + 4z2 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. 4x2 + -2y + y2 + 2y + 4z2 = 0 + 2y Reorder the terms: 4x2 + -2y + 2y + y2 + 4z2 = 0 + 2y Combine like terms: -2y + 2y = 0 4x2 + 0 + y2 + 4z2 = 0 + 2y 4x2 + y2 + 4z2 = 0 + 2y Remove the zero: 4x2 + y2 + 4z2 = 2y Add '-1y2' to each side of the equation. 4x2 + y2 + -1y2 + 4z2 = 2y + -1y2 Combine like terms: y2 + -1y2 = 0 4x2 + 0 + 4z2 = 2y + -1y2 4x2 + 4z2 = 2y + -1y2 Add '-4z2' to each side of the equation. 4x2 + 4z2 + -4z2 = 2y + -1y2 + -4z2 Combine like terms: 4z2 + -4z2 = 0 4x2 + 0 = 2y + -1y2 + -4z2 4x2 = 2y + -1y2 + -4z2 Divide each side by '4'. x2 = 0.5y + -0.25y2 + -1z2 Simplifying x2 = 0.5y + -0.25y2 + -1z2 Reorder the terms: x2 + -0.5y + 0.25y2 + z2 = 0.5y + -0.5y + -0.25y2 + 0.25y2 + -1z2 + z2 Combine like terms: 0.5y + -0.5y = 0.0 x2 + -0.5y + 0.25y2 + z2 = 0.0 + -0.25y2 + 0.25y2 + -1z2 + z2 x2 + -0.5y + 0.25y2 + z2 = -0.25y2 + 0.25y2 + -1z2 + z2 Combine like terms: -0.25y2 + 0.25y2 = 0.00 x2 + -0.5y + 0.25y2 + z2 = 0.00 + -1z2 + z2 x2 + -0.5y + 0.25y2 + z2 = -1z2 + z2 Combine like terms: -1z2 + z2 = 0 x2 + -0.5y + 0.25y2 + z2 = 0 The solution to this equation could not be determined.
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