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Simplifying 2x2 + -5x + 2 = (x + -3)(x + -2) + 3x Reorder the terms: 2 + -5x + 2x2 = (x + -3)(x + -2) + 3x Reorder the terms: 2 + -5x + 2x2 = (-3 + x)(x + -2) + 3x Reorder the terms: 2 + -5x + 2x2 = (-3 + x)(-2 + x) + 3x Multiply (-3 + x) * (-2 + x) 2 + -5x + 2x2 = (-3(-2 + x) + x(-2 + x)) + 3x 2 + -5x + 2x2 = ((-2 * -3 + x * -3) + x(-2 + x)) + 3x 2 + -5x + 2x2 = ((6 + -3x) + x(-2 + x)) + 3x 2 + -5x + 2x2 = (6 + -3x + (-2 * x + x * x)) + 3x 2 + -5x + 2x2 = (6 + -3x + (-2x + x2)) + 3x Combine like terms: -3x + -2x = -5x 2 + -5x + 2x2 = (6 + -5x + x2) + 3x Reorder the terms: 2 + -5x + 2x2 = 6 + -5x + 3x + x2 Combine like terms: -5x + 3x = -2x 2 + -5x + 2x2 = 6 + -2x + x2 Solving 2 + -5x + 2x2 = 6 + -2x + x2 Solving for variable 'x'. Reorder the terms: 2 + -6 + -5x + 2x + 2x2 + -1x2 = 6 + -2x + x2 + -6 + 2x + -1x2 Combine like terms: 2 + -6 = -4 -4 + -5x + 2x + 2x2 + -1x2 = 6 + -2x + x2 + -6 + 2x + -1x2 Combine like terms: -5x + 2x = -3x -4 + -3x + 2x2 + -1x2 = 6 + -2x + x2 + -6 + 2x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -4 + -3x + 1x2 = 6 + -2x + x2 + -6 + 2x + -1x2 Reorder the terms: -4 + -3x + 1x2 = 6 + -6 + -2x + 2x + x2 + -1x2 Combine like terms: 6 + -6 = 0 -4 + -3x + 1x2 = 0 + -2x + 2x + x2 + -1x2 -4 + -3x + 1x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 -4 + -3x + 1x2 = 0 + x2 + -1x2 -4 + -3x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -4 + -3x + 1x2 = 0 Factor a trinomial. (-1 + -1x)(4 + -1x) = 0Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-1, 4}
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