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Simplifying (x + -1)(2x + -1) = 28 Reorder the terms: (-1 + x)(2x + -1) = 28 Reorder the terms: (-1 + x)(-1 + 2x) = 28 Multiply (-1 + x) * (-1 + 2x) (-1(-1 + 2x) + x(-1 + 2x)) = 28 ((-1 * -1 + 2x * -1) + x(-1 + 2x)) = 28 ((1 + -2x) + x(-1 + 2x)) = 28 (1 + -2x + (-1 * x + 2x * x)) = 28 (1 + -2x + (-1x + 2x2)) = 28 Combine like terms: -2x + -1x = -3x (1 + -3x + 2x2) = 28 Solving 1 + -3x + 2x2 = 28 Solving for variable 'x'. Reorder the terms: 1 + -28 + -3x + 2x2 = 28 + -28 Combine like terms: 1 + -28 = -27 -27 + -3x + 2x2 = 28 + -28 Combine like terms: 28 + -28 = 0 -27 + -3x + 2x2 = 0 Factor a trinomial. (-3 + -1x)(9 + -2x) = 0Subproblem 1
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 = -3Subproblem 2
Set the factor '(9 + -2x)' equal to zero and attempt to solve: Simplifying 9 + -2x = 0 Solving 9 + -2x = 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 + -2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2x = 0 + -9 -2x = 0 + -9 Combine like terms: 0 + -9 = -9 -2x = -9 Divide each side by '-2'. x = 4.5 Simplifying x = 4.5Solution
x = {-3, 4.5}
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