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Simplifying x2 + 6x + -11 = 7x + -5 Reorder the terms: -11 + 6x + x2 = 7x + -5 Reorder the terms: -11 + 6x + x2 = -5 + 7x Solving -11 + 6x + x2 = -5 + 7x Solving for variable 'x'. Reorder the terms: -11 + 5 + 6x + -7x + x2 = -5 + 7x + 5 + -7x Combine like terms: -11 + 5 = -6 -6 + 6x + -7x + x2 = -5 + 7x + 5 + -7x Combine like terms: 6x + -7x = -1x -6 + -1x + x2 = -5 + 7x + 5 + -7x Reorder the terms: -6 + -1x + x2 = -5 + 5 + 7x + -7x Combine like terms: -5 + 5 = 0 -6 + -1x + x2 = 0 + 7x + -7x -6 + -1x + x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -6 + -1x + x2 = 0 Factor a trinomial. (-2 + -1x)(3 + -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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-2, 3}
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