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Simplifying 1 + -5x = 49 + 14x + x2 Solving 1 + -5x = 49 + 14x + x2 Solving for variable 'x'. Reorder the terms: 1 + -49 + -5x + -14x + -1x2 = 49 + 14x + x2 + -49 + -14x + -1x2 Combine like terms: 1 + -49 = -48 -48 + -5x + -14x + -1x2 = 49 + 14x + x2 + -49 + -14x + -1x2 Combine like terms: -5x + -14x = -19x -48 + -19x + -1x2 = 49 + 14x + x2 + -49 + -14x + -1x2 Reorder the terms: -48 + -19x + -1x2 = 49 + -49 + 14x + -14x + x2 + -1x2 Combine like terms: 49 + -49 = 0 -48 + -19x + -1x2 = 0 + 14x + -14x + x2 + -1x2 -48 + -19x + -1x2 = 14x + -14x + x2 + -1x2 Combine like terms: 14x + -14x = 0 -48 + -19x + -1x2 = 0 + x2 + -1x2 -48 + -19x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -48 + -19x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(48 + 19x + x2) = 0 Factor a trinomial. -1((16 + x)(3 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(16 + x)' equal to zero and attempt to solve: Simplifying 16 + x = 0 Solving 16 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 0 + -16 Combine like terms: 16 + -16 = 0 0 + x = 0 + -16 x = 0 + -16 Combine like terms: 0 + -16 = -16 x = -16 Simplifying x = -16Subproblem 2
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 = -3Solution
x = {-16, -3}
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