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Simplifying 2x2 + -5x + -2 = (x + -2)(x + -2) Reorder the terms: -2 + -5x + 2x2 = (x + -2)(x + -2) Reorder the terms: -2 + -5x + 2x2 = (-2 + x)(x + -2) Reorder the terms: -2 + -5x + 2x2 = (-2 + x)(-2 + x) Multiply (-2 + x) * (-2 + x) -2 + -5x + 2x2 = (-2(-2 + x) + x(-2 + x)) -2 + -5x + 2x2 = ((-2 * -2 + x * -2) + x(-2 + x)) -2 + -5x + 2x2 = ((4 + -2x) + x(-2 + x)) -2 + -5x + 2x2 = (4 + -2x + (-2 * x + x * x)) -2 + -5x + 2x2 = (4 + -2x + (-2x + x2)) Combine like terms: -2x + -2x = -4x -2 + -5x + 2x2 = (4 + -4x + x2) Solving -2 + -5x + 2x2 = 4 + -4x + x2 Solving for variable 'x'. Reorder the terms: -2 + -4 + -5x + 4x + 2x2 + -1x2 = 4 + -4x + x2 + -4 + 4x + -1x2 Combine like terms: -2 + -4 = -6 -6 + -5x + 4x + 2x2 + -1x2 = 4 + -4x + x2 + -4 + 4x + -1x2 Combine like terms: -5x + 4x = -1x -6 + -1x + 2x2 + -1x2 = 4 + -4x + x2 + -4 + 4x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -6 + -1x + 1x2 = 4 + -4x + x2 + -4 + 4x + -1x2 Reorder the terms: -6 + -1x + 1x2 = 4 + -4 + -4x + 4x + x2 + -1x2 Combine like terms: 4 + -4 = 0 -6 + -1x + 1x2 = 0 + -4x + 4x + x2 + -1x2 -6 + -1x + 1x2 = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 0 -6 + -1x + 1x2 = 0 + x2 + -1x2 -6 + -1x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -6 + -1x + 1x2 = 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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