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