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Simplifying 4x4 + 8x2 + 9 = 0 Reorder the terms: 9 + 8x2 + 4x4 = 0 Solving 9 + 8x2 + 4x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + 2x2 + x4 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 2x2 + -2.25 + x4 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 2x2 + x4 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 2x2 + x4 = 0 + -2.25 2x2 + x4 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 2x2 + x4 = -2.25 The x term is 2x2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x2 + 1 + x4 = -2.25 + 1 Reorder the terms: 1 + 2x2 + x4 = -2.25 + 1 Combine like terms: -2.25 + 1 = -1.25 1 + 2x2 + x4 = -1.25 Factor a perfect square on the left side: (x2 + 1)(x2 + 1) = -1.25 Can't calculate square root of the right side. The solution to this equation could not be determined.
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