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Simplifying 3x + -5 = 2x2 + 19x + 27 Reorder the terms: -5 + 3x = 2x2 + 19x + 27 Reorder the terms: -5 + 3x = 27 + 19x + 2x2 Solving -5 + 3x = 27 + 19x + 2x2 Solving for variable 'x'. Reorder the terms: -5 + -27 + 3x + -19x + -2x2 = 27 + 19x + 2x2 + -27 + -19x + -2x2 Combine like terms: -5 + -27 = -32 -32 + 3x + -19x + -2x2 = 27 + 19x + 2x2 + -27 + -19x + -2x2 Combine like terms: 3x + -19x = -16x -32 + -16x + -2x2 = 27 + 19x + 2x2 + -27 + -19x + -2x2 Reorder the terms: -32 + -16x + -2x2 = 27 + -27 + 19x + -19x + 2x2 + -2x2 Combine like terms: 27 + -27 = 0 -32 + -16x + -2x2 = 0 + 19x + -19x + 2x2 + -2x2 -32 + -16x + -2x2 = 19x + -19x + 2x2 + -2x2 Combine like terms: 19x + -19x = 0 -32 + -16x + -2x2 = 0 + 2x2 + -2x2 -32 + -16x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -32 + -16x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(16 + 8x + x2) = 0 Factor a trinomial. -2((4 + x)(4 + x)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {-4, -4}
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