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Simplifying (x + 4)(2x + 3) = (3x)(7 + -4x) + (2x + 1) Reorder the terms: (4 + x)(2x + 3) = (3x)(7 + -4x) + (2x + 1) Reorder the terms: (4 + x)(3 + 2x) = (3x)(7 + -4x) + (2x + 1) Multiply (4 + x) * (3 + 2x) (4(3 + 2x) + x(3 + 2x)) = (3x)(7 + -4x) + (2x + 1) ((3 * 4 + 2x * 4) + x(3 + 2x)) = (3x)(7 + -4x) + (2x + 1) ((12 + 8x) + x(3 + 2x)) = (3x)(7 + -4x) + (2x + 1) (12 + 8x + (3 * x + 2x * x)) = (3x)(7 + -4x) + (2x + 1) (12 + 8x + (3x + 2x2)) = (3x)(7 + -4x) + (2x + 1) Combine like terms: 8x + 3x = 11x (12 + 11x + 2x2) = (3x)(7 + -4x) + (2x + 1) Remove parenthesis around (3x) 12 + 11x + 2x2 = 3x(7 + -4x) + (2x + 1) 12 + 11x + 2x2 = (7 * 3x + -4x * 3x) + (2x + 1) 12 + 11x + 2x2 = (21x + -12x2) + (2x + 1) Reorder the terms: 12 + 11x + 2x2 = 21x + -12x2 + (1 + 2x) Remove parenthesis around (1 + 2x) 12 + 11x + 2x2 = 21x + -12x2 + 1 + 2x Reorder the terms: 12 + 11x + 2x2 = 1 + 21x + 2x + -12x2 Combine like terms: 21x + 2x = 23x 12 + 11x + 2x2 = 1 + 23x + -12x2 Solving 12 + 11x + 2x2 = 1 + 23x + -12x2 Solving for variable 'x'. Reorder the terms: 12 + -1 + 11x + -23x + 2x2 + 12x2 = 1 + 23x + -12x2 + -1 + -23x + 12x2 Combine like terms: 12 + -1 = 11 11 + 11x + -23x + 2x2 + 12x2 = 1 + 23x + -12x2 + -1 + -23x + 12x2 Combine like terms: 11x + -23x = -12x 11 + -12x + 2x2 + 12x2 = 1 + 23x + -12x2 + -1 + -23x + 12x2 Combine like terms: 2x2 + 12x2 = 14x2 11 + -12x + 14x2 = 1 + 23x + -12x2 + -1 + -23x + 12x2 Reorder the terms: 11 + -12x + 14x2 = 1 + -1 + 23x + -23x + -12x2 + 12x2 Combine like terms: 1 + -1 = 0 11 + -12x + 14x2 = 0 + 23x + -23x + -12x2 + 12x2 11 + -12x + 14x2 = 23x + -23x + -12x2 + 12x2 Combine like terms: 23x + -23x = 0 11 + -12x + 14x2 = 0 + -12x2 + 12x2 11 + -12x + 14x2 = -12x2 + 12x2 Combine like terms: -12x2 + 12x2 = 0 11 + -12x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 0.7857142857 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '-0.7857142857' to each side of the equation. 0.7857142857 + -0.8571428571x + -0.7857142857 + x2 = 0 + -0.7857142857 Reorder the terms: 0.7857142857 + -0.7857142857 + -0.8571428571x + x2 = 0 + -0.7857142857 Combine like terms: 0.7857142857 + -0.7857142857 = 0.0000000000 0.0000000000 + -0.8571428571x + x2 = 0 + -0.7857142857 -0.8571428571x + x2 = 0 + -0.7857142857 Combine like terms: 0 + -0.7857142857 = -0.7857142857 -0.8571428571x + x2 = -0.7857142857 The x term is -0.8571428571x. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571x + 0.1836734694 + x2 = -0.7857142857 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = -0.7857142857 + 0.1836734694 Combine like terms: -0.7857142857 + 0.1836734694 = -0.6020408163 0.1836734694 + -0.8571428571x + x2 = -0.6020408163 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = -0.6020408163 Can't calculate square root of the right side. The solution to this equation could not be determined.
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