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Simplifying (x + 9)(x + -5) = (2x + 8)(x + -5) Reorder the terms: (9 + x)(x + -5) = (2x + 8)(x + -5) Reorder the terms: (9 + x)(-5 + x) = (2x + 8)(x + -5) Multiply (9 + x) * (-5 + x) (9(-5 + x) + x(-5 + x)) = (2x + 8)(x + -5) ((-5 * 9 + x * 9) + x(-5 + x)) = (2x + 8)(x + -5) ((-45 + 9x) + x(-5 + x)) = (2x + 8)(x + -5) (-45 + 9x + (-5 * x + x * x)) = (2x + 8)(x + -5) (-45 + 9x + (-5x + x2)) = (2x + 8)(x + -5) Combine like terms: 9x + -5x = 4x (-45 + 4x + x2) = (2x + 8)(x + -5) Reorder the terms: -45 + 4x + x2 = (8 + 2x)(x + -5) Reorder the terms: -45 + 4x + x2 = (8 + 2x)(-5 + x) Multiply (8 + 2x) * (-5 + x) -45 + 4x + x2 = (8(-5 + x) + 2x * (-5 + x)) -45 + 4x + x2 = ((-5 * 8 + x * 8) + 2x * (-5 + x)) -45 + 4x + x2 = ((-40 + 8x) + 2x * (-5 + x)) -45 + 4x + x2 = (-40 + 8x + (-5 * 2x + x * 2x)) -45 + 4x + x2 = (-40 + 8x + (-10x + 2x2)) Combine like terms: 8x + -10x = -2x -45 + 4x + x2 = (-40 + -2x + 2x2) Solving -45 + 4x + x2 = -40 + -2x + 2x2 Solving for variable 'x'. Reorder the terms: -45 + 40 + 4x + 2x + x2 + -2x2 = -40 + -2x + 2x2 + 40 + 2x + -2x2 Combine like terms: -45 + 40 = -5 -5 + 4x + 2x + x2 + -2x2 = -40 + -2x + 2x2 + 40 + 2x + -2x2 Combine like terms: 4x + 2x = 6x -5 + 6x + x2 + -2x2 = -40 + -2x + 2x2 + 40 + 2x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -5 + 6x + -1x2 = -40 + -2x + 2x2 + 40 + 2x + -2x2 Reorder the terms: -5 + 6x + -1x2 = -40 + 40 + -2x + 2x + 2x2 + -2x2 Combine like terms: -40 + 40 = 0 -5 + 6x + -1x2 = 0 + -2x + 2x + 2x2 + -2x2 -5 + 6x + -1x2 = -2x + 2x + 2x2 + -2x2 Combine like terms: -2x + 2x = 0 -5 + 6x + -1x2 = 0 + 2x2 + -2x2 -5 + 6x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -5 + 6x + -1x2 = 0 Factor a trinomial. (-5 + x)(1 + -1x) = 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 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {5, 1}
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