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Simplifying 0 = 7x4 + -2x2 + 1 Reorder the terms: 0 = 1 + -2x2 + 7x4 Solving 0 = 1 + -2x2 + 7x4 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + 2x2 + -7x4 = 1 + -2x2 + 7x4 + -1 + 2x2 + -7x4 Reorder the terms: -1 + 2x2 + -7x4 = 1 + -1 + -2x2 + 2x2 + 7x4 + -7x4 Combine like terms: 1 + -1 = 0 -1 + 2x2 + -7x4 = 0 + -2x2 + 2x2 + 7x4 + -7x4 -1 + 2x2 + -7x4 = -2x2 + 2x2 + 7x4 + -7x4 Combine like terms: -2x2 + 2x2 = 0 -1 + 2x2 + -7x4 = 0 + 7x4 + -7x4 -1 + 2x2 + -7x4 = 7x4 + -7x4 Combine like terms: 7x4 + -7x4 = 0 -1 + 2x2 + -7x4 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 0.1428571429 + -0.2857142857x2 + x4 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.2857142857x2 + -0.1428571429 + x4 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + -0.2857142857x2 + x4 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + -0.2857142857x2 + x4 = 0 + -0.1428571429 -0.2857142857x2 + x4 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 -0.2857142857x2 + x4 = -0.1428571429 The x term is -0.2857142857x2. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857x2 + 0.02040816328 + x4 = -0.1428571429 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x2 + x4 = -0.1428571429 + 0.02040816328 Combine like terms: -0.1428571429 + 0.02040816328 = -0.12244897962 0.02040816328 + -0.2857142857x2 + x4 = -0.12244897962 Factor a perfect square on the left side: (x2 + -0.1428571429)(x2 + -0.1428571429) = -0.12244897962 Can't calculate square root of the right side. The solution to this equation could not be determined.
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