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Simplifying (x + -11)(x + -3) = 9 Reorder the terms: (-11 + x)(x + -3) = 9 Reorder the terms: (-11 + x)(-3 + x) = 9 Multiply (-11 + x) * (-3 + x) (-11(-3 + x) + x(-3 + x)) = 9 ((-3 * -11 + x * -11) + x(-3 + x)) = 9 ((33 + -11x) + x(-3 + x)) = 9 (33 + -11x + (-3 * x + x * x)) = 9 (33 + -11x + (-3x + x2)) = 9 Combine like terms: -11x + -3x = -14x (33 + -14x + x2) = 9 Solving 33 + -14x + x2 = 9 Solving for variable 'x'. Reorder the terms: 33 + -9 + -14x + x2 = 9 + -9 Combine like terms: 33 + -9 = 24 24 + -14x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 24 + -14x + x2 = 0 Factor a trinomial. (2 + -1x)(12 + -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 '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Divide each side by '-1'. x = 12 Simplifying x = 12Solution
x = {2, 12}
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