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Simplifying (x + 8)(x + -5) = -42 Reorder the terms: (8 + x)(x + -5) = -42 Reorder the terms: (8 + x)(-5 + x) = -42 Multiply (8 + x) * (-5 + x) (8(-5 + x) + x(-5 + x)) = -42 ((-5 * 8 + x * 8) + x(-5 + x)) = -42 ((-40 + 8x) + x(-5 + x)) = -42 (-40 + 8x + (-5 * x + x * x)) = -42 (-40 + 8x + (-5x + x2)) = -42 Combine like terms: 8x + -5x = 3x (-40 + 3x + x2) = -42 Solving -40 + 3x + x2 = -42 Solving for variable 'x'. Reorder the terms: -40 + 42 + 3x + x2 = -42 + 42 Combine like terms: -40 + 42 = 2 2 + 3x + x2 = -42 + 42 Combine like terms: -42 + 42 = 0 2 + 3x + x2 = 0 Factor a trinomial. (2 + x)(1 + x) = 0Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 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 = {-2, -1}
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