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Simplifying 0 = x4 + -6x2 + 25 Reorder the terms: 0 = 25 + -6x2 + x4 Solving 0 = 25 + -6x2 + x4 Solving for variable 'x'. Combine like terms: 0 + -25 = -25 -25 + 6x2 + -1x4 = 25 + -6x2 + x4 + -25 + 6x2 + -1x4 Reorder the terms: -25 + 6x2 + -1x4 = 25 + -25 + -6x2 + 6x2 + x4 + -1x4 Combine like terms: 25 + -25 = 0 -25 + 6x2 + -1x4 = 0 + -6x2 + 6x2 + x4 + -1x4 -25 + 6x2 + -1x4 = -6x2 + 6x2 + x4 + -1x4 Combine like terms: -6x2 + 6x2 = 0 -25 + 6x2 + -1x4 = 0 + x4 + -1x4 -25 + 6x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 -25 + 6x2 + -1x4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 25 + -6x2 + x4 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + -6x2 + -25 + x4 = 0 + -25 Reorder the terms: 25 + -25 + -6x2 + x4 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -6x2 + x4 = 0 + -25 -6x2 + x4 = 0 + -25 Combine like terms: 0 + -25 = -25 -6x2 + x4 = -25 The x term is -6x2. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x2 + 9 + x4 = -25 + 9 Reorder the terms: 9 + -6x2 + x4 = -25 + 9 Combine like terms: -25 + 9 = -16 9 + -6x2 + x4 = -16 Factor a perfect square on the left side: (x2 + -3)(x2 + -3) = -16 Can't calculate square root of the right side. The solution to this equation could not be determined.
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