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Simplifying 8x + -40 + 8x + -40 = 18(x + -5)(2x + -10) Reorder the terms: -40 + -40 + 8x + 8x = 18(x + -5)(2x + -10) Combine like terms: -40 + -40 = -80 -80 + 8x + 8x = 18(x + -5)(2x + -10) Combine like terms: 8x + 8x = 16x -80 + 16x = 18(x + -5)(2x + -10) Reorder the terms: -80 + 16x = 18(-5 + x)(2x + -10) Reorder the terms: -80 + 16x = 18(-5 + x)(-10 + 2x) Multiply (-5 + x) * (-10 + 2x) -80 + 16x = 18(-5(-10 + 2x) + x(-10 + 2x)) -80 + 16x = 18((-10 * -5 + 2x * -5) + x(-10 + 2x)) -80 + 16x = 18((50 + -10x) + x(-10 + 2x)) -80 + 16x = 18(50 + -10x + (-10 * x + 2x * x)) -80 + 16x = 18(50 + -10x + (-10x + 2x2)) Combine like terms: -10x + -10x = -20x -80 + 16x = 18(50 + -20x + 2x2) -80 + 16x = (50 * 18 + -20x * 18 + 2x2 * 18) -80 + 16x = (900 + -360x + 36x2) Solving -80 + 16x = 900 + -360x + 36x2 Solving for variable 'x'. Reorder the terms: -80 + -900 + 16x + 360x + -36x2 = 900 + -360x + 36x2 + -900 + 360x + -36x2 Combine like terms: -80 + -900 = -980 -980 + 16x + 360x + -36x2 = 900 + -360x + 36x2 + -900 + 360x + -36x2 Combine like terms: 16x + 360x = 376x -980 + 376x + -36x2 = 900 + -360x + 36x2 + -900 + 360x + -36x2 Reorder the terms: -980 + 376x + -36x2 = 900 + -900 + -360x + 360x + 36x2 + -36x2 Combine like terms: 900 + -900 = 0 -980 + 376x + -36x2 = 0 + -360x + 360x + 36x2 + -36x2 -980 + 376x + -36x2 = -360x + 360x + 36x2 + -36x2 Combine like terms: -360x + 360x = 0 -980 + 376x + -36x2 = 0 + 36x2 + -36x2 -980 + 376x + -36x2 = 36x2 + -36x2 Combine like terms: 36x2 + -36x2 = 0 -980 + 376x + -36x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-245 + 94x + -9x2) = 0 Factor a trinomial. 4((-49 + 9x)(5 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-49 + 9x)' equal to zero and attempt to solve: Simplifying -49 + 9x = 0 Solving -49 + 9x = 0 Move all terms containing x to the left, all other terms to the right. Add '49' to each side of the equation. -49 + 49 + 9x = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 9x = 0 + 49 9x = 0 + 49 Combine like terms: 0 + 49 = 49 9x = 49 Divide each side by '9'. x = 5.444444444 Simplifying x = 5.444444444Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {5.444444444, 5}
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