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Simplifying (x + 7)(x + -1) = x2 + 1 + 2x Reorder the terms: (7 + x)(x + -1) = x2 + 1 + 2x Reorder the terms: (7 + x)(-1 + x) = x2 + 1 + 2x Multiply (7 + x) * (-1 + x) (7(-1 + x) + x(-1 + x)) = x2 + 1 + 2x ((-1 * 7 + x * 7) + x(-1 + x)) = x2 + 1 + 2x ((-7 + 7x) + x(-1 + x)) = x2 + 1 + 2x (-7 + 7x + (-1 * x + x * x)) = x2 + 1 + 2x (-7 + 7x + (-1x + x2)) = x2 + 1 + 2x Combine like terms: 7x + -1x = 6x (-7 + 6x + x2) = x2 + 1 + 2x Reorder the terms: -7 + 6x + x2 = 1 + 2x + x2 Add '-1x2' to each side of the equation. -7 + 6x + x2 + -1x2 = 1 + 2x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -7 + 6x + 0 = 1 + 2x + x2 + -1x2 -7 + 6x = 1 + 2x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -7 + 6x = 1 + 2x + 0 -7 + 6x = 1 + 2x Solving -7 + 6x = 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 + 6x + -2x = 1 + 2x + -2x Combine like terms: 6x + -2x = 4x -7 + 4x = 1 + 2x + -2x Combine like terms: 2x + -2x = 0 -7 + 4x = 1 + 0 -7 + 4x = 1 Add '7' to each side of the equation. -7 + 7 + 4x = 1 + 7 Combine like terms: -7 + 7 = 0 0 + 4x = 1 + 7 4x = 1 + 7 Combine like terms: 1 + 7 = 8 4x = 8 Divide each side by '4'. x = 2 Simplifying x = 2
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