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Simplifying (4x + -1)(15x + -31) = -1(8x + 92) Reorder the terms: (-1 + 4x)(15x + -31) = -1(8x + 92) Reorder the terms: (-1 + 4x)(-31 + 15x) = -1(8x + 92) Multiply (-1 + 4x) * (-31 + 15x) (-1(-31 + 15x) + 4x * (-31 + 15x)) = -1(8x + 92) ((-31 * -1 + 15x * -1) + 4x * (-31 + 15x)) = -1(8x + 92) ((31 + -15x) + 4x * (-31 + 15x)) = -1(8x + 92) (31 + -15x + (-31 * 4x + 15x * 4x)) = -1(8x + 92) (31 + -15x + (-124x + 60x2)) = -1(8x + 92) Combine like terms: -15x + -124x = -139x (31 + -139x + 60x2) = -1(8x + 92) Reorder the terms: 31 + -139x + 60x2 = -1(92 + 8x) 31 + -139x + 60x2 = (92 * -1 + 8x * -1) 31 + -139x + 60x2 = (-92 + -8x) Solving 31 + -139x + 60x2 = -92 + -8x Solving for variable 'x'. Reorder the terms: 31 + 92 + -139x + 8x + 60x2 = -92 + -8x + 92 + 8x Combine like terms: 31 + 92 = 123 123 + -139x + 8x + 60x2 = -92 + -8x + 92 + 8x Combine like terms: -139x + 8x = -131x 123 + -131x + 60x2 = -92 + -8x + 92 + 8x Reorder the terms: 123 + -131x + 60x2 = -92 + 92 + -8x + 8x Combine like terms: -92 + 92 = 0 123 + -131x + 60x2 = 0 + -8x + 8x 123 + -131x + 60x2 = -8x + 8x Combine like terms: -8x + 8x = 0 123 + -131x + 60x2 = 0 Begin completing the square. Divide all terms by 60 the coefficient of the squared term: Divide each side by '60'. 2.05 + -2.183333333x + x2 = 0.0 Move the constant term to the right: Add '-2.05' to each side of the equation. 2.05 + -2.183333333x + -2.05 + x2 = 0.0 + -2.05 Reorder the terms: 2.05 + -2.05 + -2.183333333x + x2 = 0.0 + -2.05 Combine like terms: 2.05 + -2.05 = 0.00 0.00 + -2.183333333x + x2 = 0.0 + -2.05 -2.183333333x + x2 = 0.0 + -2.05 Combine like terms: 0.0 + -2.05 = -2.05 -2.183333333x + x2 = -2.05 The x term is -2.183333333x. Take half its coefficient (-1.091666667). Square it (1.191736112) and add it to both sides. Add '1.191736112' to each side of the equation. -2.183333333x + 1.191736112 + x2 = -2.05 + 1.191736112 Reorder the terms: 1.191736112 + -2.183333333x + x2 = -2.05 + 1.191736112 Combine like terms: -2.05 + 1.191736112 = -0.858263888 1.191736112 + -2.183333333x + x2 = -0.858263888 Factor a perfect square on the left side: (x + -1.091666667)(x + -1.091666667) = -0.858263888 Can't calculate square root of the right side. The solution to this equation could not be determined.
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