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Simplifying (x + 7)(x + 3) = x(x + 20) + 1 Reorder the terms: (7 + x)(x + 3) = x(x + 20) + 1 Reorder the terms: (7 + x)(3 + x) = x(x + 20) + 1 Multiply (7 + x) * (3 + x) (7(3 + x) + x(3 + x)) = x(x + 20) + 1 ((3 * 7 + x * 7) + x(3 + x)) = x(x + 20) + 1 ((21 + 7x) + x(3 + x)) = x(x + 20) + 1 (21 + 7x + (3 * x + x * x)) = x(x + 20) + 1 (21 + 7x + (3x + x2)) = x(x + 20) + 1 Combine like terms: 7x + 3x = 10x (21 + 10x + x2) = x(x + 20) + 1 Reorder the terms: 21 + 10x + x2 = x(20 + x) + 1 21 + 10x + x2 = (20 * x + x * x) + 1 21 + 10x + x2 = (20x + x2) + 1 Reorder the terms: 21 + 10x + x2 = 1 + 20x + x2 Add '-1x2' to each side of the equation. 21 + 10x + x2 + -1x2 = 1 + 20x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 21 + 10x + 0 = 1 + 20x + x2 + -1x2 21 + 10x = 1 + 20x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 21 + 10x = 1 + 20x + 0 21 + 10x = 1 + 20x Solving 21 + 10x = 1 + 20x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20x' to each side of the equation. 21 + 10x + -20x = 1 + 20x + -20x Combine like terms: 10x + -20x = -10x 21 + -10x = 1 + 20x + -20x Combine like terms: 20x + -20x = 0 21 + -10x = 1 + 0 21 + -10x = 1 Add '-21' to each side of the equation. 21 + -21 + -10x = 1 + -21 Combine like terms: 21 + -21 = 0 0 + -10x = 1 + -21 -10x = 1 + -21 Combine like terms: 1 + -21 = -20 -10x = -20 Divide each side by '-10'. x = 2 Simplifying x = 2
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