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Simplifying 2x4 + -6x2 + 9 = 0 Reorder the terms: 9 + -6x2 + 2x4 = 0 Solving 9 + -6x2 + 2x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + -3x2 + x4 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -3x2 + -4.5 + x4 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -3x2 + x4 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -3x2 + x4 = 0 + -4.5 -3x2 + x4 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -3x2 + x4 = -4.5 The x term is -3x2. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x2 + 2.25 + x4 = -4.5 + 2.25 Reorder the terms: 2.25 + -3x2 + x4 = -4.5 + 2.25 Combine like terms: -4.5 + 2.25 = -2.25 2.25 + -3x2 + x4 = -2.25 Factor a perfect square on the left side: (x2 + -1.5)(x2 + -1.5) = -2.25 Can't calculate square root of the right side. The solution to this equation could not be determined.
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