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Simplifying (x + -3)(2 + -1x) + -3(2 + -1x) = 5(x + 1) Reorder the terms: (-3 + x)(2 + -1x) + -3(2 + -1x) = 5(x + 1) Multiply (-3 + x) * (2 + -1x) (-3(2 + -1x) + x(2 + -1x)) + -3(2 + -1x) = 5(x + 1) ((2 * -3 + -1x * -3) + x(2 + -1x)) + -3(2 + -1x) = 5(x + 1) ((-6 + 3x) + x(2 + -1x)) + -3(2 + -1x) = 5(x + 1) (-6 + 3x + (2 * x + -1x * x)) + -3(2 + -1x) = 5(x + 1) (-6 + 3x + (2x + -1x2)) + -3(2 + -1x) = 5(x + 1) Combine like terms: 3x + 2x = 5x (-6 + 5x + -1x2) + -3(2 + -1x) = 5(x + 1) -6 + 5x + -1x2 + (2 * -3 + -1x * -3) = 5(x + 1) -6 + 5x + -1x2 + (-6 + 3x) = 5(x + 1) Reorder the terms: -6 + -6 + 5x + 3x + -1x2 = 5(x + 1) Combine like terms: -6 + -6 = -12 -12 + 5x + 3x + -1x2 = 5(x + 1) Combine like terms: 5x + 3x = 8x -12 + 8x + -1x2 = 5(x + 1) Reorder the terms: -12 + 8x + -1x2 = 5(1 + x) -12 + 8x + -1x2 = (1 * 5 + x * 5) -12 + 8x + -1x2 = (5 + 5x) Solving -12 + 8x + -1x2 = 5 + 5x Solving for variable 'x'. Reorder the terms: -12 + -5 + 8x + -5x + -1x2 = 5 + 5x + -5 + -5x Combine like terms: -12 + -5 = -17 -17 + 8x + -5x + -1x2 = 5 + 5x + -5 + -5x Combine like terms: 8x + -5x = 3x -17 + 3x + -1x2 = 5 + 5x + -5 + -5x Reorder the terms: -17 + 3x + -1x2 = 5 + -5 + 5x + -5x Combine like terms: 5 + -5 = 0 -17 + 3x + -1x2 = 0 + 5x + -5x -17 + 3x + -1x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -17 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 17 + -3x + x2 = 0 Move the constant term to the right: Add '-17' to each side of the equation. 17 + -3x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + -3x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -3x + x2 = 0 + -17 -3x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 -3x + x2 = -17 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -17 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -17 + 2.25 Combine like terms: -17 + 2.25 = -14.75 2.25 + -3x + x2 = -14.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -14.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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