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Simplifying (x + -4)(x + -4) = 2x2 + -12x + 19 Reorder the terms: (-4 + x)(x + -4) = 2x2 + -12x + 19 Reorder the terms: (-4 + x)(-4 + x) = 2x2 + -12x + 19 Multiply (-4 + x) * (-4 + x) (-4(-4 + x) + x(-4 + x)) = 2x2 + -12x + 19 ((-4 * -4 + x * -4) + x(-4 + x)) = 2x2 + -12x + 19 ((16 + -4x) + x(-4 + x)) = 2x2 + -12x + 19 (16 + -4x + (-4 * x + x * x)) = 2x2 + -12x + 19 (16 + -4x + (-4x + x2)) = 2x2 + -12x + 19 Combine like terms: -4x + -4x = -8x (16 + -8x + x2) = 2x2 + -12x + 19 Reorder the terms: 16 + -8x + x2 = 19 + -12x + 2x2 Solving 16 + -8x + x2 = 19 + -12x + 2x2 Solving for variable 'x'. Reorder the terms: 16 + -19 + -8x + 12x + x2 + -2x2 = 19 + -12x + 2x2 + -19 + 12x + -2x2 Combine like terms: 16 + -19 = -3 -3 + -8x + 12x + x2 + -2x2 = 19 + -12x + 2x2 + -19 + 12x + -2x2 Combine like terms: -8x + 12x = 4x -3 + 4x + x2 + -2x2 = 19 + -12x + 2x2 + -19 + 12x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -3 + 4x + -1x2 = 19 + -12x + 2x2 + -19 + 12x + -2x2 Reorder the terms: -3 + 4x + -1x2 = 19 + -19 + -12x + 12x + 2x2 + -2x2 Combine like terms: 19 + -19 = 0 -3 + 4x + -1x2 = 0 + -12x + 12x + 2x2 + -2x2 -3 + 4x + -1x2 = -12x + 12x + 2x2 + -2x2 Combine like terms: -12x + 12x = 0 -3 + 4x + -1x2 = 0 + 2x2 + -2x2 -3 + 4x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -3 + 4x + -1x2 = 0 Factor a trinomial. (-3 + x)(1 + -1x) = 0Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 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 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3Subproblem 2
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 = 1Solution
x = {3, 1}
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