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Simplifying (3x + 7)(x + 0.5) = (0.4x + -10)(0.1x + 6) Reorder the terms: (7 + 3x)(x + 0.5) = (0.4x + -10)(0.1x + 6) Reorder the terms: (7 + 3x)(0.5 + x) = (0.4x + -10)(0.1x + 6) Multiply (7 + 3x) * (0.5 + x) (7(0.5 + x) + 3x * (0.5 + x)) = (0.4x + -10)(0.1x + 6) ((0.5 * 7 + x * 7) + 3x * (0.5 + x)) = (0.4x + -10)(0.1x + 6) ((3.5 + 7x) + 3x * (0.5 + x)) = (0.4x + -10)(0.1x + 6) (3.5 + 7x + (0.5 * 3x + x * 3x)) = (0.4x + -10)(0.1x + 6) (3.5 + 7x + (1.5x + 3x2)) = (0.4x + -10)(0.1x + 6) Combine like terms: 7x + 1.5x = 8.5x (3.5 + 8.5x + 3x2) = (0.4x + -10)(0.1x + 6) Reorder the terms: 3.5 + 8.5x + 3x2 = (-10 + 0.4x)(0.1x + 6) Reorder the terms: 3.5 + 8.5x + 3x2 = (-10 + 0.4x)(6 + 0.1x) Multiply (-10 + 0.4x) * (6 + 0.1x) 3.5 + 8.5x + 3x2 = (-10(6 + 0.1x) + 0.4x * (6 + 0.1x)) 3.5 + 8.5x + 3x2 = ((6 * -10 + 0.1x * -10) + 0.4x * (6 + 0.1x)) 3.5 + 8.5x + 3x2 = ((-60 + -1x) + 0.4x * (6 + 0.1x)) 3.5 + 8.5x + 3x2 = (-60 + -1x + (6 * 0.4x + 0.1x * 0.4x)) 3.5 + 8.5x + 3x2 = (-60 + -1x + (2.4x + 0.04x2)) Combine like terms: -1x + 2.4x = 1.4x 3.5 + 8.5x + 3x2 = (-60 + 1.4x + 0.04x2) Solving 3.5 + 8.5x + 3x2 = -60 + 1.4x + 0.04x2 Solving for variable 'x'. Reorder the terms: 3.5 + 60 + 8.5x + -1.4x + 3x2 + -0.04x2 = -60 + 1.4x + 0.04x2 + 60 + -1.4x + -0.04x2 Combine like terms: 3.5 + 60 = 63.5 63.5 + 8.5x + -1.4x + 3x2 + -0.04x2 = -60 + 1.4x + 0.04x2 + 60 + -1.4x + -0.04x2 Combine like terms: 8.5x + -1.4x = 7.1x 63.5 + 7.1x + 3x2 + -0.04x2 = -60 + 1.4x + 0.04x2 + 60 + -1.4x + -0.04x2 Combine like terms: 3x2 + -0.04x2 = 2.96x2 63.5 + 7.1x + 2.96x2 = -60 + 1.4x + 0.04x2 + 60 + -1.4x + -0.04x2 Reorder the terms: 63.5 + 7.1x + 2.96x2 = -60 + 60 + 1.4x + -1.4x + 0.04x2 + -0.04x2 Combine like terms: -60 + 60 = 0 63.5 + 7.1x + 2.96x2 = 0 + 1.4x + -1.4x + 0.04x2 + -0.04x2 63.5 + 7.1x + 2.96x2 = 1.4x + -1.4x + 0.04x2 + -0.04x2 Combine like terms: 1.4x + -1.4x = 0.0 63.5 + 7.1x + 2.96x2 = 0.0 + 0.04x2 + -0.04x2 63.5 + 7.1x + 2.96x2 = 0.04x2 + -0.04x2 Combine like terms: 0.04x2 + -0.04x2 = 0.00 63.5 + 7.1x + 2.96x2 = 0.00 Begin completing the square. Divide all terms by 2.96 the coefficient of the squared term: Divide each side by '2.96'. 21.4527027 + 2.398648649x + x2 = 0 Move the constant term to the right: Add '-21.4527027' to each side of the equation. 21.4527027 + 2.398648649x + -21.4527027 + x2 = 0 + -21.4527027 Reorder the terms: 21.4527027 + -21.4527027 + 2.398648649x + x2 = 0 + -21.4527027 Combine like terms: 21.4527027 + -21.4527027 = 0.0000000 0.0000000 + 2.398648649x + x2 = 0 + -21.4527027 2.398648649x + x2 = 0 + -21.4527027 Combine like terms: 0 + -21.4527027 = -21.4527027 2.398648649x + x2 = -21.4527027 The x term is 2.398648649x. Take half its coefficient (1.199324325). Square it (1.438378837) and add it to both sides. Add '1.438378837' to each side of the equation. 2.398648649x + 1.438378837 + x2 = -21.4527027 + 1.438378837 Reorder the terms: 1.438378837 + 2.398648649x + x2 = -21.4527027 + 1.438378837 Combine like terms: -21.4527027 + 1.438378837 = -20.014323863 1.438378837 + 2.398648649x + x2 = -20.014323863 Factor a perfect square on the left side: (x + 1.199324325)(x + 1.199324325) = -20.014323863 Can't calculate square root of the right side. The solution to this equation could not be determined.
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