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Simplifying (x + -1)(x + 4) = (x + -5) Reorder the terms: (-1 + x)(x + 4) = (x + -5) Reorder the terms: (-1 + x)(4 + x) = (x + -5) Multiply (-1 + x) * (4 + x) (-1(4 + x) + x(4 + x)) = (x + -5) ((4 * -1 + x * -1) + x(4 + x)) = (x + -5) ((-4 + -1x) + x(4 + x)) = (x + -5) (-4 + -1x + (4 * x + x * x)) = (x + -5) (-4 + -1x + (4x + x2)) = (x + -5) Combine like terms: -1x + 4x = 3x (-4 + 3x + x2) = (x + -5) Reorder the terms: -4 + 3x + x2 = (-5 + x) Remove parenthesis around (-5 + x) -4 + 3x + x2 = -5 + x Solving -4 + 3x + x2 = -5 + x Solving for variable 'x'. Reorder the terms: -4 + 5 + 3x + -1x + x2 = -5 + x + 5 + -1x Combine like terms: -4 + 5 = 1 1 + 3x + -1x + x2 = -5 + x + 5 + -1x Combine like terms: 3x + -1x = 2x 1 + 2x + x2 = -5 + x + 5 + -1x Reorder the terms: 1 + 2x + x2 = -5 + 5 + x + -1x Combine like terms: -5 + 5 = 0 1 + 2x + x2 = 0 + x + -1x 1 + 2x + x2 = x + -1x Combine like terms: x + -1x = 0 1 + 2x + x2 = 0 Factor a trinomial. (1 + x)(1 + x) = 0Subproblem 1
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 = -1Subproblem 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 = {-1, -1}
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