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Simplifying (x + 7)(x + 3) + -1(-9x + -3)(x + 2) = 0 Reorder the terms: (7 + x)(x + 3) + -1(-9x + -3)(x + 2) = 0 Reorder the terms: (7 + x)(3 + x) + -1(-9x + -3)(x + 2) = 0 Multiply (7 + x) * (3 + x) (7(3 + x) + x(3 + x)) + -1(-9x + -3)(x + 2) = 0 ((3 * 7 + x * 7) + x(3 + x)) + -1(-9x + -3)(x + 2) = 0 ((21 + 7x) + x(3 + x)) + -1(-9x + -3)(x + 2) = 0 (21 + 7x + (3 * x + x * x)) + -1(-9x + -3)(x + 2) = 0 (21 + 7x + (3x + x2)) + -1(-9x + -3)(x + 2) = 0 Combine like terms: 7x + 3x = 10x (21 + 10x + x2) + -1(-9x + -3)(x + 2) = 0 Reorder the terms: 21 + 10x + x2 + -1(-3 + -9x)(x + 2) = 0 Reorder the terms: 21 + 10x + x2 + -1(-3 + -9x)(2 + x) = 0 Multiply (-3 + -9x) * (2 + x) 21 + 10x + x2 + -1(-3(2 + x) + -9x * (2 + x)) = 0 21 + 10x + x2 + -1((2 * -3 + x * -3) + -9x * (2 + x)) = 0 21 + 10x + x2 + -1((-6 + -3x) + -9x * (2 + x)) = 0 21 + 10x + x2 + -1(-6 + -3x + (2 * -9x + x * -9x)) = 0 21 + 10x + x2 + -1(-6 + -3x + (-18x + -9x2)) = 0 Combine like terms: -3x + -18x = -21x 21 + 10x + x2 + -1(-6 + -21x + -9x2) = 0 21 + 10x + x2 + (-6 * -1 + -21x * -1 + -9x2 * -1) = 0 21 + 10x + x2 + (6 + 21x + 9x2) = 0 Reorder the terms: 21 + 6 + 10x + 21x + x2 + 9x2 = 0 Combine like terms: 21 + 6 = 27 27 + 10x + 21x + x2 + 9x2 = 0 Combine like terms: 10x + 21x = 31x 27 + 31x + x2 + 9x2 = 0 Combine like terms: x2 + 9x2 = 10x2 27 + 31x + 10x2 = 0 Solving 27 + 31x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 2.7 + 3.1x + x2 = 0.0 Move the constant term to the right: Add '-2.7' to each side of the equation. 2.7 + 3.1x + -2.7 + x2 = 0.0 + -2.7 Reorder the terms: 2.7 + -2.7 + 3.1x + x2 = 0.0 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + 3.1x + x2 = 0.0 + -2.7 3.1x + x2 = 0.0 + -2.7 Combine like terms: 0.0 + -2.7 = -2.7 3.1x + x2 = -2.7 The x term is 3.1x. Take half its coefficient (1.55). Square it (2.4025) and add it to both sides. Add '2.4025' to each side of the equation. 3.1x + 2.4025 + x2 = -2.7 + 2.4025 Reorder the terms: 2.4025 + 3.1x + x2 = -2.7 + 2.4025 Combine like terms: -2.7 + 2.4025 = -0.2975 2.4025 + 3.1x + x2 = -0.2975 Factor a perfect square on the left side: (x + 1.55)(x + 1.55) = -0.2975 Can't calculate square root of the right side. The solution to this equation could not be determined.
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