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Simplifying (x + -3)(x + -10) = 8 Reorder the terms: (-3 + x)(x + -10) = 8 Reorder the terms: (-3 + x)(-10 + x) = 8 Multiply (-3 + x) * (-10 + x) (-3(-10 + x) + x(-10 + x)) = 8 ((-10 * -3 + x * -3) + x(-10 + x)) = 8 ((30 + -3x) + x(-10 + x)) = 8 (30 + -3x + (-10 * x + x * x)) = 8 (30 + -3x + (-10x + x2)) = 8 Combine like terms: -3x + -10x = -13x (30 + -13x + x2) = 8 Solving 30 + -13x + x2 = 8 Solving for variable 'x'. Reorder the terms: 30 + -8 + -13x + x2 = 8 + -8 Combine like terms: 30 + -8 = 22 22 + -13x + x2 = 8 + -8 Combine like terms: 8 + -8 = 0 22 + -13x + x2 = 0 Factor a trinomial. (2 + -1x)(11 + -1x) = 0Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve: Simplifying 11 + -1x = 0 Solving 11 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1x = 0 + -11 -1x = 0 + -11 Combine like terms: 0 + -11 = -11 -1x = -11 Divide each side by '-1'. x = 11 Simplifying x = 11Solution
x = {2, 11}
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