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Simplifying (3x + 2)(3x + 2) = (x + 2)(x + -3) Reorder the terms: (2 + 3x)(3x + 2) = (x + 2)(x + -3) Reorder the terms: (2 + 3x)(2 + 3x) = (x + 2)(x + -3) Multiply (2 + 3x) * (2 + 3x) (2(2 + 3x) + 3x * (2 + 3x)) = (x + 2)(x + -3) ((2 * 2 + 3x * 2) + 3x * (2 + 3x)) = (x + 2)(x + -3) ((4 + 6x) + 3x * (2 + 3x)) = (x + 2)(x + -3) (4 + 6x + (2 * 3x + 3x * 3x)) = (x + 2)(x + -3) (4 + 6x + (6x + 9x2)) = (x + 2)(x + -3) Combine like terms: 6x + 6x = 12x (4 + 12x + 9x2) = (x + 2)(x + -3) Reorder the terms: 4 + 12x + 9x2 = (2 + x)(x + -3) Reorder the terms: 4 + 12x + 9x2 = (2 + x)(-3 + x) Multiply (2 + x) * (-3 + x) 4 + 12x + 9x2 = (2(-3 + x) + x(-3 + x)) 4 + 12x + 9x2 = ((-3 * 2 + x * 2) + x(-3 + x)) 4 + 12x + 9x2 = ((-6 + 2x) + x(-3 + x)) 4 + 12x + 9x2 = (-6 + 2x + (-3 * x + x * x)) 4 + 12x + 9x2 = (-6 + 2x + (-3x + x2)) Combine like terms: 2x + -3x = -1x 4 + 12x + 9x2 = (-6 + -1x + x2) Solving 4 + 12x + 9x2 = -6 + -1x + x2 Solving for variable 'x'. Reorder the terms: 4 + 6 + 12x + x + 9x2 + -1x2 = -6 + -1x + x2 + 6 + x + -1x2 Combine like terms: 4 + 6 = 10 10 + 12x + x + 9x2 + -1x2 = -6 + -1x + x2 + 6 + x + -1x2 Combine like terms: 12x + x = 13x 10 + 13x + 9x2 + -1x2 = -6 + -1x + x2 + 6 + x + -1x2 Combine like terms: 9x2 + -1x2 = 8x2 10 + 13x + 8x2 = -6 + -1x + x2 + 6 + x + -1x2 Reorder the terms: 10 + 13x + 8x2 = -6 + 6 + -1x + x + x2 + -1x2 Combine like terms: -6 + 6 = 0 10 + 13x + 8x2 = 0 + -1x + x + x2 + -1x2 10 + 13x + 8x2 = -1x + x + x2 + -1x2 Combine like terms: -1x + x = 0 10 + 13x + 8x2 = 0 + x2 + -1x2 10 + 13x + 8x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 10 + 13x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.25 + 1.625x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 1.625x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 1.625x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 1.625x + x2 = 0 + -1.25 1.625x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 1.625x + x2 = -1.25 The x term is 1.625x. Take half its coefficient (0.8125). Square it (0.66015625) and add it to both sides. Add '0.66015625' to each side of the equation. 1.625x + 0.66015625 + x2 = -1.25 + 0.66015625 Reorder the terms: 0.66015625 + 1.625x + x2 = -1.25 + 0.66015625 Combine like terms: -1.25 + 0.66015625 = -0.58984375 0.66015625 + 1.625x + x2 = -0.58984375 Factor a perfect square on the left side: (x + 0.8125)(x + 0.8125) = -0.58984375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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