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Simplifying (x + 10)(x + -4) = -45 Reorder the terms: (10 + x)(x + -4) = -45 Reorder the terms: (10 + x)(-4 + x) = -45 Multiply (10 + x) * (-4 + x) (10(-4 + x) + x(-4 + x)) = -45 ((-4 * 10 + x * 10) + x(-4 + x)) = -45 ((-40 + 10x) + x(-4 + x)) = -45 (-40 + 10x + (-4 * x + x * x)) = -45 (-40 + 10x + (-4x + x2)) = -45 Combine like terms: 10x + -4x = 6x (-40 + 6x + x2) = -45 Solving -40 + 6x + x2 = -45 Solving for variable 'x'. Reorder the terms: -40 + 45 + 6x + x2 = -45 + 45 Combine like terms: -40 + 45 = 5 5 + 6x + x2 = -45 + 45 Combine like terms: -45 + 45 = 0 5 + 6x + x2 = 0 Factor a trinomial. (5 + x)(1 + x) = 0Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 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 = {-5, -1}
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