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Simplifying 5x2 + -3y2 + 3x2 + -5z2 + -3y2 + 2z2 = 0 Reorder the terms: 5x2 + 3x2 + -3y2 + -3y2 + -5z2 + 2z2 = 0 Combine like terms: 5x2 + 3x2 = 8x2 8x2 + -3y2 + -3y2 + -5z2 + 2z2 = 0 Combine like terms: -3y2 + -3y2 = -6y2 8x2 + -6y2 + -5z2 + 2z2 = 0 Combine like terms: -5z2 + 2z2 = -3z2 8x2 + -6y2 + -3z2 = 0 Solving 8x2 + -6y2 + -3z2 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6y2' to each side of the equation. 8x2 + -6y2 + 6y2 + -3z2 = 0 + 6y2 Combine like terms: -6y2 + 6y2 = 0 8x2 + 0 + -3z2 = 0 + 6y2 8x2 + -3z2 = 0 + 6y2 Remove the zero: 8x2 + -3z2 = 6y2 Add '3z2' to each side of the equation. 8x2 + -3z2 + 3z2 = 6y2 + 3z2 Combine like terms: -3z2 + 3z2 = 0 8x2 + 0 = 6y2 + 3z2 8x2 = 6y2 + 3z2 Divide each side by '8'. x2 = 0.75y2 + 0.375z2 Simplifying x2 = 0.75y2 + 0.375z2 Reorder the terms: x2 + -0.75y2 + -0.375z2 = 0.75y2 + -0.75y2 + 0.375z2 + -0.375z2 Combine like terms: 0.75y2 + -0.75y2 = 0.00 x2 + -0.75y2 + -0.375z2 = 0.00 + 0.375z2 + -0.375z2 x2 + -0.75y2 + -0.375z2 = 0.375z2 + -0.375z2 Combine like terms: 0.375z2 + -0.375z2 = 0.000 x2 + -0.75y2 + -0.375z2 = 0.000 The solution to this equation could not be determined.
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