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Simplifying (7x + -3)(x + 2) + -4x = 5(3x + -2) Reorder the terms: (-3 + 7x)(x + 2) + -4x = 5(3x + -2) Reorder the terms: (-3 + 7x)(2 + x) + -4x = 5(3x + -2) Multiply (-3 + 7x) * (2 + x) (-3(2 + x) + 7x * (2 + x)) + -4x = 5(3x + -2) ((2 * -3 + x * -3) + 7x * (2 + x)) + -4x = 5(3x + -2) ((-6 + -3x) + 7x * (2 + x)) + -4x = 5(3x + -2) (-6 + -3x + (2 * 7x + x * 7x)) + -4x = 5(3x + -2) (-6 + -3x + (14x + 7x2)) + -4x = 5(3x + -2) Combine like terms: -3x + 14x = 11x (-6 + 11x + 7x2) + -4x = 5(3x + -2) Reorder the terms: -6 + 11x + -4x + 7x2 = 5(3x + -2) Combine like terms: 11x + -4x = 7x -6 + 7x + 7x2 = 5(3x + -2) Reorder the terms: -6 + 7x + 7x2 = 5(-2 + 3x) -6 + 7x + 7x2 = (-2 * 5 + 3x * 5) -6 + 7x + 7x2 = (-10 + 15x) Solving -6 + 7x + 7x2 = -10 + 15x Solving for variable 'x'. Reorder the terms: -6 + 10 + 7x + -15x + 7x2 = -10 + 15x + 10 + -15x Combine like terms: -6 + 10 = 4 4 + 7x + -15x + 7x2 = -10 + 15x + 10 + -15x Combine like terms: 7x + -15x = -8x 4 + -8x + 7x2 = -10 + 15x + 10 + -15x Reorder the terms: 4 + -8x + 7x2 = -10 + 10 + 15x + -15x Combine like terms: -10 + 10 = 0 4 + -8x + 7x2 = 0 + 15x + -15x 4 + -8x + 7x2 = 15x + -15x Combine like terms: 15x + -15x = 0 4 + -8x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.5714285714 + -1.142857143x + x2 = 0 Move the constant term to the right: Add '-0.5714285714' to each side of the equation. 0.5714285714 + -1.142857143x + -0.5714285714 + x2 = 0 + -0.5714285714 Reorder the terms: 0.5714285714 + -0.5714285714 + -1.142857143x + x2 = 0 + -0.5714285714 Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000 0.0000000000 + -1.142857143x + x2 = 0 + -0.5714285714 -1.142857143x + x2 = 0 + -0.5714285714 Combine like terms: 0 + -0.5714285714 = -0.5714285714 -1.142857143x + x2 = -0.5714285714 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 = -0.5714285714 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143x + x2 = -0.5714285714 + 0.3265306123 Combine like terms: -0.5714285714 + 0.3265306123 = -0.2448979591 0.3265306123 + -1.142857143x + x2 = -0.2448979591 Factor a perfect square on the left side: (x + -0.5714285715)(x + -0.5714285715) = -0.2448979591 Can't calculate square root of the right side. The solution to this equation could not be determined.
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