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Simplifying x2 + -3x + 27 = 8x + -3 Reorder the terms: 27 + -3x + x2 = 8x + -3 Reorder the terms: 27 + -3x + x2 = -3 + 8x Solving 27 + -3x + x2 = -3 + 8x Solving for variable 'x'. Reorder the terms: 27 + 3 + -3x + -8x + x2 = -3 + 8x + 3 + -8x Combine like terms: 27 + 3 = 30 30 + -3x + -8x + x2 = -3 + 8x + 3 + -8x Combine like terms: -3x + -8x = -11x 30 + -11x + x2 = -3 + 8x + 3 + -8x Reorder the terms: 30 + -11x + x2 = -3 + 3 + 8x + -8x Combine like terms: -3 + 3 = 0 30 + -11x + x2 = 0 + 8x + -8x 30 + -11x + x2 = 8x + -8x Combine like terms: 8x + -8x = 0 30 + -11x + x2 = 0 Factor a trinomial. (5 + -1x)(6 + -1x) = 0Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {5, 6}
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