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Simplifying 4x2 + 3y2 + 4z2 + 8z = 0 Reorder the terms: 4x2 + 3y2 + 8z + 4z2 = 0 Solving 4x2 + 3y2 + 8z + 4z2 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3y2' to each side of the equation. 4x2 + 3y2 + 8z + -3y2 + 4z2 = 0 + -3y2 Reorder the terms: 4x2 + 3y2 + -3y2 + 8z + 4z2 = 0 + -3y2 Combine like terms: 3y2 + -3y2 = 0 4x2 + 0 + 8z + 4z2 = 0 + -3y2 4x2 + 8z + 4z2 = 0 + -3y2 Remove the zero: 4x2 + 8z + 4z2 = -3y2 Add '-8z' to each side of the equation. 4x2 + 8z + -8z + 4z2 = -3y2 + -8z Combine like terms: 8z + -8z = 0 4x2 + 0 + 4z2 = -3y2 + -8z 4x2 + 4z2 = -3y2 + -8z Add '-4z2' to each side of the equation. 4x2 + 4z2 + -4z2 = -3y2 + -8z + -4z2 Combine like terms: 4z2 + -4z2 = 0 4x2 + 0 = -3y2 + -8z + -4z2 4x2 = -3y2 + -8z + -4z2 Divide each side by '4'. x2 = -0.75y2 + -2z + -1z2 Simplifying x2 = -0.75y2 + -2z + -1z2 Reorder the terms: x2 + 0.75y2 + 2z + z2 = -0.75y2 + 0.75y2 + -2z + 2z + -1z2 + z2 Combine like terms: -0.75y2 + 0.75y2 = 0.00 x2 + 0.75y2 + 2z + z2 = 0.00 + -2z + 2z + -1z2 + z2 x2 + 0.75y2 + 2z + z2 = -2z + 2z + -1z2 + z2 Combine like terms: -2z + 2z = 0 x2 + 0.75y2 + 2z + z2 = 0 + -1z2 + z2 x2 + 0.75y2 + 2z + z2 = -1z2 + z2 Combine like terms: -1z2 + z2 = 0 x2 + 0.75y2 + 2z + z2 = 0 The solution to this equation could not be determined.
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