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Simplifying 5(x + -3) + -1(3x + 2)(x + -2) + -7x = -3(x + 1) Reorder the terms: 5(-3 + x) + -1(3x + 2)(x + -2) + -7x = -3(x + 1) (-3 * 5 + x * 5) + -1(3x + 2)(x + -2) + -7x = -3(x + 1) (-15 + 5x) + -1(3x + 2)(x + -2) + -7x = -3(x + 1) Reorder the terms: -15 + 5x + -1(2 + 3x)(x + -2) + -7x = -3(x + 1) Reorder the terms: -15 + 5x + -1(2 + 3x)(-2 + x) + -7x = -3(x + 1) Multiply (2 + 3x) * (-2 + x) -15 + 5x + -1(2(-2 + x) + 3x * (-2 + x)) + -7x = -3(x + 1) -15 + 5x + -1((-2 * 2 + x * 2) + 3x * (-2 + x)) + -7x = -3(x + 1) -15 + 5x + -1((-4 + 2x) + 3x * (-2 + x)) + -7x = -3(x + 1) -15 + 5x + -1(-4 + 2x + (-2 * 3x + x * 3x)) + -7x = -3(x + 1) -15 + 5x + -1(-4 + 2x + (-6x + 3x2)) + -7x = -3(x + 1) Combine like terms: 2x + -6x = -4x -15 + 5x + -1(-4 + -4x + 3x2) + -7x = -3(x + 1) -15 + 5x + (-4 * -1 + -4x * -1 + 3x2 * -1) + -7x = -3(x + 1) -15 + 5x + (4 + 4x + -3x2) + -7x = -3(x + 1) Reorder the terms: -15 + 4 + 5x + 4x + -7x + -3x2 = -3(x + 1) Combine like terms: -15 + 4 = -11 -11 + 5x + 4x + -7x + -3x2 = -3(x + 1) Combine like terms: 5x + 4x = 9x -11 + 9x + -7x + -3x2 = -3(x + 1) Combine like terms: 9x + -7x = 2x -11 + 2x + -3x2 = -3(x + 1) Reorder the terms: -11 + 2x + -3x2 = -3(1 + x) -11 + 2x + -3x2 = (1 * -3 + x * -3) -11 + 2x + -3x2 = (-3 + -3x) Solving -11 + 2x + -3x2 = -3 + -3x Solving for variable 'x'. Reorder the terms: -11 + 3 + 2x + 3x + -3x2 = -3 + -3x + 3 + 3x Combine like terms: -11 + 3 = -8 -8 + 2x + 3x + -3x2 = -3 + -3x + 3 + 3x Combine like terms: 2x + 3x = 5x -8 + 5x + -3x2 = -3 + -3x + 3 + 3x Reorder the terms: -8 + 5x + -3x2 = -3 + 3 + -3x + 3x Combine like terms: -3 + 3 = 0 -8 + 5x + -3x2 = 0 + -3x + 3x -8 + 5x + -3x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -8 + 5x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 2.666666667 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + -1.666666667x + -2.666666667 + x2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + -1.666666667x + x2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + -1.666666667x + x2 = 0 + -2.666666667 -1.666666667x + x2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 -1.666666667x + x2 = -2.666666667 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = -2.666666667 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = -2.666666667 + 0.6944444447 Combine like terms: -2.666666667 + 0.6944444447 = -1.9722222223 0.6944444447 + -1.666666667x + x2 = -1.9722222223 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = -1.9722222223 Can't calculate square root of the right side. The solution to this equation could not be determined.
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