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Simplifying (x + 5)(x + -1) + (x + -3)(x + -1) = (x + 1)(x + -3) Reorder the terms: (5 + x)(x + -1) + (x + -3)(x + -1) = (x + 1)(x + -3) Reorder the terms: (5 + x)(-1 + x) + (x + -3)(x + -1) = (x + 1)(x + -3) Multiply (5 + x) * (-1 + x) (5(-1 + x) + x(-1 + x)) + (x + -3)(x + -1) = (x + 1)(x + -3) ((-1 * 5 + x * 5) + x(-1 + x)) + (x + -3)(x + -1) = (x + 1)(x + -3) ((-5 + 5x) + x(-1 + x)) + (x + -3)(x + -1) = (x + 1)(x + -3) (-5 + 5x + (-1 * x + x * x)) + (x + -3)(x + -1) = (x + 1)(x + -3) (-5 + 5x + (-1x + x2)) + (x + -3)(x + -1) = (x + 1)(x + -3) Combine like terms: 5x + -1x = 4x (-5 + 4x + x2) + (x + -3)(x + -1) = (x + 1)(x + -3) Reorder the terms: -5 + 4x + x2 + (-3 + x)(x + -1) = (x + 1)(x + -3) Reorder the terms: -5 + 4x + x2 + (-3 + x)(-1 + x) = (x + 1)(x + -3) Multiply (-3 + x) * (-1 + x) -5 + 4x + x2 + (-3(-1 + x) + x(-1 + x)) = (x + 1)(x + -3) -5 + 4x + x2 + ((-1 * -3 + x * -3) + x(-1 + x)) = (x + 1)(x + -3) -5 + 4x + x2 + ((3 + -3x) + x(-1 + x)) = (x + 1)(x + -3) -5 + 4x + x2 + (3 + -3x + (-1 * x + x * x)) = (x + 1)(x + -3) -5 + 4x + x2 + (3 + -3x + (-1x + x2)) = (x + 1)(x + -3) Combine like terms: -3x + -1x = -4x -5 + 4x + x2 + (3 + -4x + x2) = (x + 1)(x + -3) Reorder the terms: -5 + 3 + 4x + -4x + x2 + x2 = (x + 1)(x + -3) Combine like terms: -5 + 3 = -2 -2 + 4x + -4x + x2 + x2 = (x + 1)(x + -3) Combine like terms: 4x + -4x = 0 -2 + 0 + x2 + x2 = (x + 1)(x + -3) -2 + x2 + x2 = (x + 1)(x + -3) Combine like terms: x2 + x2 = 2x2 -2 + 2x2 = (x + 1)(x + -3) Reorder the terms: -2 + 2x2 = (1 + x)(x + -3) Reorder the terms: -2 + 2x2 = (1 + x)(-3 + x) Multiply (1 + x) * (-3 + x) -2 + 2x2 = (1(-3 + x) + x(-3 + x)) -2 + 2x2 = ((-3 * 1 + x * 1) + x(-3 + x)) -2 + 2x2 = ((-3 + 1x) + x(-3 + x)) -2 + 2x2 = (-3 + 1x + (-3 * x + x * x)) -2 + 2x2 = (-3 + 1x + (-3x + x2)) Combine like terms: 1x + -3x = -2x -2 + 2x2 = (-3 + -2x + x2) Solving -2 + 2x2 = -3 + -2x + x2 Solving for variable 'x'. Reorder the terms: -2 + 3 + 2x + 2x2 + -1x2 = -3 + -2x + x2 + 3 + 2x + -1x2 Combine like terms: -2 + 3 = 1 1 + 2x + 2x2 + -1x2 = -3 + -2x + x2 + 3 + 2x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 1 + 2x + 1x2 = -3 + -2x + x2 + 3 + 2x + -1x2 Reorder the terms: 1 + 2x + 1x2 = -3 + 3 + -2x + 2x + x2 + -1x2 Combine like terms: -3 + 3 = 0 1 + 2x + 1x2 = 0 + -2x + 2x + x2 + -1x2 1 + 2x + 1x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 1 + 2x + 1x2 = 0 + x2 + -1x2 1 + 2x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1 + 2x + 1x2 = 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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