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Simplifying (X + 7)(X + 1) = (X + 1)(X + 1) Reorder the terms: (7 + X)(X + 1) = (X + 1)(X + 1) Reorder the terms: (7 + X)(1 + X) = (X + 1)(X + 1) Multiply (7 + X) * (1 + X) (7(1 + X) + X(1 + X)) = (X + 1)(X + 1) ((1 * 7 + X * 7) + X(1 + X)) = (X + 1)(X + 1) ((7 + 7X) + X(1 + X)) = (X + 1)(X + 1) (7 + 7X + (1 * X + X * X)) = (X + 1)(X + 1) (7 + 7X + (1X + X2)) = (X + 1)(X + 1) Combine like terms: 7X + 1X = 8X (7 + 8X + X2) = (X + 1)(X + 1) Reorder the terms: 7 + 8X + X2 = (1 + X)(X + 1) Reorder the terms: 7 + 8X + X2 = (1 + X)(1 + X) Multiply (1 + X) * (1 + X) 7 + 8X + X2 = (1(1 + X) + X(1 + X)) 7 + 8X + X2 = ((1 * 1 + X * 1) + X(1 + X)) 7 + 8X + X2 = ((1 + 1X) + X(1 + X)) 7 + 8X + X2 = (1 + 1X + (1 * X + X * X)) 7 + 8X + X2 = (1 + 1X + (1X + X2)) Combine like terms: 1X + 1X = 2X 7 + 8X + X2 = (1 + 2X + X2) Add '-1X2' to each side of the equation. 7 + 8X + X2 + -1X2 = 1 + 2X + X2 + -1X2 Combine like terms: X2 + -1X2 = 0 7 + 8X + 0 = 1 + 2X + X2 + -1X2 7 + 8X = 1 + 2X + X2 + -1X2 Combine like terms: X2 + -1X2 = 0 7 + 8X = 1 + 2X + 0 7 + 8X = 1 + 2X Solving 7 + 8X = 1 + 2X Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2X' to each side of the equation. 7 + 8X + -2X = 1 + 2X + -2X Combine like terms: 8X + -2X = 6X 7 + 6X = 1 + 2X + -2X Combine like terms: 2X + -2X = 0 7 + 6X = 1 + 0 7 + 6X = 1 Add '-7' to each side of the equation. 7 + -7 + 6X = 1 + -7 Combine like terms: 7 + -7 = 0 0 + 6X = 1 + -7 6X = 1 + -7 Combine like terms: 1 + -7 = -6 6X = -6 Divide each side by '6'. X = -1 Simplifying X = -1
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