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Simplifying 17x + 4 = (x + 3)(2x + 7) + -1x + 8 Reorder the terms: 4 + 17x = (x + 3)(2x + 7) + -1x + 8 Reorder the terms: 4 + 17x = (3 + x)(2x + 7) + -1x + 8 Reorder the terms: 4 + 17x = (3 + x)(7 + 2x) + -1x + 8 Multiply (3 + x) * (7 + 2x) 4 + 17x = (3(7 + 2x) + x(7 + 2x)) + -1x + 8 4 + 17x = ((7 * 3 + 2x * 3) + x(7 + 2x)) + -1x + 8 4 + 17x = ((21 + 6x) + x(7 + 2x)) + -1x + 8 4 + 17x = (21 + 6x + (7 * x + 2x * x)) + -1x + 8 4 + 17x = (21 + 6x + (7x + 2x2)) + -1x + 8 Combine like terms: 6x + 7x = 13x 4 + 17x = (21 + 13x + 2x2) + -1x + 8 Reorder the terms: 4 + 17x = 21 + 8 + 13x + -1x + 2x2 Combine like terms: 21 + 8 = 29 4 + 17x = 29 + 13x + -1x + 2x2 Combine like terms: 13x + -1x = 12x 4 + 17x = 29 + 12x + 2x2 Solving 4 + 17x = 29 + 12x + 2x2 Solving for variable 'x'. Reorder the terms: 4 + -29 + 17x + -12x + -2x2 = 29 + 12x + 2x2 + -29 + -12x + -2x2 Combine like terms: 4 + -29 = -25 -25 + 17x + -12x + -2x2 = 29 + 12x + 2x2 + -29 + -12x + -2x2 Combine like terms: 17x + -12x = 5x -25 + 5x + -2x2 = 29 + 12x + 2x2 + -29 + -12x + -2x2 Reorder the terms: -25 + 5x + -2x2 = 29 + -29 + 12x + -12x + 2x2 + -2x2 Combine like terms: 29 + -29 = 0 -25 + 5x + -2x2 = 0 + 12x + -12x + 2x2 + -2x2 -25 + 5x + -2x2 = 12x + -12x + 2x2 + -2x2 Combine like terms: 12x + -12x = 0 -25 + 5x + -2x2 = 0 + 2x2 + -2x2 -25 + 5x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -25 + 5x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 12.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -2.5x + -12.5 + x2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -2.5x + x2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -2.5x + x2 = 0 + -12.5 -2.5x + x2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -2.5x + x2 = -12.5 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -12.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -12.5 + 1.5625 Combine like terms: -12.5 + 1.5625 = -10.9375 1.5625 + -2.5x + x2 = -10.9375 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = -10.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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