# (x-2)(x-8)=7

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## Solution for (x-2)(x-8)=7 equation:

Simplifying (x + -2)(x + -8) = 7 Reorder the terms: (-2 + x)(x + -8) = 7 Reorder the terms: (-2 + x)(-8 + x) = 7 Multiply (-2 + x) * (-8 + x) (-2(-8 + x) + x(-8 + x)) = 7 ((-8 * -2 + x * -2) + x(-8 + x)) = 7 ((16 + -2x) + x(-8 + x)) = 7 (16 + -2x + (-8 * x + x * x)) = 7 (16 + -2x + (-8x + x^{2})) = 7 Combine like terms: -2x + -8x = -10x (16 + -10x + x^{2}) = 7 Solving 16 + -10x + x^{2}= 7 Solving for variable 'x'. Reorder the terms: 16 + -7 + -10x + x^{2}= 7 + -7 Combine like terms: 16 + -7 = 9 9 + -10x + x^{2}= 7 + -7 Combine like terms: 7 + -7 = 0 9 + -10x + x^{2}= 0 Factor a trinomial. (1 + -1x)(9 + -1x) = 0## Subproblem 1

Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1## Subproblem 2

Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9## Solution

x = {1, 9}

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