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Simplifying 0 = (3x + -1)(3 + -1x) + 4x2 + 19 Reorder the terms: 0 = (-1 + 3x)(3 + -1x) + 4x2 + 19 Multiply (-1 + 3x) * (3 + -1x) 0 = (-1(3 + -1x) + 3x * (3 + -1x)) + 4x2 + 19 0 = ((3 * -1 + -1x * -1) + 3x * (3 + -1x)) + 4x2 + 19 0 = ((-3 + 1x) + 3x * (3 + -1x)) + 4x2 + 19 0 = (-3 + 1x + (3 * 3x + -1x * 3x)) + 4x2 + 19 0 = (-3 + 1x + (9x + -3x2)) + 4x2 + 19 Combine like terms: 1x + 9x = 10x 0 = (-3 + 10x + -3x2) + 4x2 + 19 Reorder the terms: 0 = -3 + 19 + 10x + -3x2 + 4x2 Combine like terms: -3 + 19 = 16 0 = 16 + 10x + -3x2 + 4x2 Combine like terms: -3x2 + 4x2 = 1x2 0 = 16 + 10x + 1x2 Solving 0 = 16 + 10x + 1x2 Solving for variable 'x'. Combine like terms: 0 + -16 = -16 -16 + -10x + -1x2 = 16 + 10x + 1x2 + -16 + -10x + -1x2 Reorder the terms: -16 + -10x + -1x2 = 16 + -16 + 10x + -10x + 1x2 + -1x2 Combine like terms: 16 + -16 = 0 -16 + -10x + -1x2 = 0 + 10x + -10x + 1x2 + -1x2 -16 + -10x + -1x2 = 10x + -10x + 1x2 + -1x2 Combine like terms: 10x + -10x = 0 -16 + -10x + -1x2 = 0 + 1x2 + -1x2 -16 + -10x + -1x2 = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 -16 + -10x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(16 + 10x + x2) = 0 Factor a trinomial. -1((8 + x)(2 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Simplifying x = -8Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-8, -2}
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