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Simplifying (3x + 1)(3 + -1x) = 4x2 + 19 Reorder the terms: (1 + 3x)(3 + -1x) = 4x2 + 19 Multiply (1 + 3x) * (3 + -1x) (1(3 + -1x) + 3x * (3 + -1x)) = 4x2 + 19 ((3 * 1 + -1x * 1) + 3x * (3 + -1x)) = 4x2 + 19 ((3 + -1x) + 3x * (3 + -1x)) = 4x2 + 19 (3 + -1x + (3 * 3x + -1x * 3x)) = 4x2 + 19 (3 + -1x + (9x + -3x2)) = 4x2 + 19 Combine like terms: -1x + 9x = 8x (3 + 8x + -3x2) = 4x2 + 19 Reorder the terms: 3 + 8x + -3x2 = 19 + 4x2 Solving 3 + 8x + -3x2 = 19 + 4x2 Solving for variable 'x'. Reorder the terms: 3 + -19 + 8x + -3x2 + -4x2 = 19 + 4x2 + -19 + -4x2 Combine like terms: 3 + -19 = -16 -16 + 8x + -3x2 + -4x2 = 19 + 4x2 + -19 + -4x2 Combine like terms: -3x2 + -4x2 = -7x2 -16 + 8x + -7x2 = 19 + 4x2 + -19 + -4x2 Reorder the terms: -16 + 8x + -7x2 = 19 + -19 + 4x2 + -4x2 Combine like terms: 19 + -19 = 0 -16 + 8x + -7x2 = 0 + 4x2 + -4x2 -16 + 8x + -7x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -16 + 8x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 2.285714286 + -1.142857143x + x2 = 0 Move the constant term to the right: Add '-2.285714286' to each side of the equation. 2.285714286 + -1.142857143x + -2.285714286 + x2 = 0 + -2.285714286 Reorder the terms: 2.285714286 + -2.285714286 + -1.142857143x + x2 = 0 + -2.285714286 Combine like terms: 2.285714286 + -2.285714286 = 0.000000000 0.000000000 + -1.142857143x + x2 = 0 + -2.285714286 -1.142857143x + x2 = 0 + -2.285714286 Combine like terms: 0 + -2.285714286 = -2.285714286 -1.142857143x + x2 = -2.285714286 The x term is -1.142857143x. Take half its coefficient (-0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. -1.142857143x + 0.3265306123 + x2 = -2.285714286 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143x + x2 = -2.285714286 + 0.3265306123 Combine like terms: -2.285714286 + 0.3265306123 = -1.9591836737 0.3265306123 + -1.142857143x + x2 = -1.9591836737 Factor a perfect square on the left side: (x + -0.5714285715)(x + -0.5714285715) = -1.9591836737 Can't calculate square root of the right side. The solution to this equation could not be determined.
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