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Simplifying 0 = (x4 + -3x2 + 2) + -1(-2x4 + x2 + -3) Reorder the terms: 0 = (2 + -3x2 + x4) + -1(-2x4 + x2 + -3) Remove parenthesis around (2 + -3x2 + x4) 0 = 2 + -3x2 + x4 + -1(-2x4 + x2 + -3) Reorder the terms: 0 = 2 + -3x2 + x4 + -1(-3 + x2 + -2x4) 0 = 2 + -3x2 + x4 + (-3 * -1 + x2 * -1 + -2x4 * -1) 0 = 2 + -3x2 + x4 + (3 + -1x2 + 2x4) Reorder the terms: 0 = 2 + 3 + -3x2 + -1x2 + x4 + 2x4 Combine like terms: 2 + 3 = 5 0 = 5 + -3x2 + -1x2 + x4 + 2x4 Combine like terms: -3x2 + -1x2 = -4x2 0 = 5 + -4x2 + x4 + 2x4 Combine like terms: x4 + 2x4 = 3x4 0 = 5 + -4x2 + 3x4 Solving 0 = 5 + -4x2 + 3x4 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + 4x2 + -3x4 = 5 + -4x2 + 3x4 + -5 + 4x2 + -3x4 Reorder the terms: -5 + 4x2 + -3x4 = 5 + -5 + -4x2 + 4x2 + 3x4 + -3x4 Combine like terms: 5 + -5 = 0 -5 + 4x2 + -3x4 = 0 + -4x2 + 4x2 + 3x4 + -3x4 -5 + 4x2 + -3x4 = -4x2 + 4x2 + 3x4 + -3x4 Combine like terms: -4x2 + 4x2 = 0 -5 + 4x2 + -3x4 = 0 + 3x4 + -3x4 -5 + 4x2 + -3x4 = 3x4 + -3x4 Combine like terms: 3x4 + -3x4 = 0 -5 + 4x2 + -3x4 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 1.666666667 + -1.333333333x2 + x4 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -1.333333333x2 + -1.666666667 + x4 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -1.333333333x2 + x4 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -1.333333333x2 + x4 = 0 + -1.666666667 -1.333333333x2 + x4 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -1.333333333x2 + x4 = -1.666666667 The x term is -1.333333333x2. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x2 + 0.4444444442 + x4 = -1.666666667 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x2 + x4 = -1.666666667 + 0.4444444442 Combine like terms: -1.666666667 + 0.4444444442 = -1.2222222228 0.4444444442 + -1.333333333x2 + x4 = -1.2222222228 Factor a perfect square on the left side: (x2 + -0.6666666665)(x2 + -0.6666666665) = -1.2222222228 Can't calculate square root of the right side. The solution to this equation could not be determined.
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