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Simplifying ((10 + -1x) * x) + ((8 + -1x) * x) = x2 + (8 + -1x)(10 + -1x) Reorder the terms for easier multiplication: (x(10 + -1x)) + ((8 + -1x) * x) = x2 + (8 + -1x)(10 + -1x) ((10 * x + -1x * x)) + ((8 + -1x) * x) = x2 + (8 + -1x)(10 + -1x) ((10x + -1x2)) + ((8 + -1x) * x) = x2 + (8 + -1x)(10 + -1x) (10x + -1x2) + ((8 + -1x) * x) = x2 + (8 + -1x)(10 + -1x) Remove parenthesis around (10x + -1x2) 10x + -1x2 + ((8 + -1x) * x) = x2 + (8 + -1x)(10 + -1x) Reorder the terms for easier multiplication: 10x + -1x2 + (x(8 + -1x)) = x2 + (8 + -1x)(10 + -1x) 10x + -1x2 + ((8 * x + -1x * x)) = x2 + (8 + -1x)(10 + -1x) 10x + -1x2 + ((8x + -1x2)) = x2 + (8 + -1x)(10 + -1x) 10x + -1x2 + (8x + -1x2) = x2 + (8 + -1x)(10 + -1x) Remove parenthesis around (8x + -1x2) 10x + -1x2 + 8x + -1x2 = x2 + (8 + -1x)(10 + -1x) Reorder the terms: 10x + 8x + -1x2 + -1x2 = x2 + (8 + -1x)(10 + -1x) Combine like terms: 10x + 8x = 18x 18x + -1x2 + -1x2 = x2 + (8 + -1x)(10 + -1x) Combine like terms: -1x2 + -1x2 = -2x2 18x + -2x2 = x2 + (8 + -1x)(10 + -1x) Multiply (8 + -1x) * (10 + -1x) 18x + -2x2 = x2 + (8(10 + -1x) + -1x * (10 + -1x)) 18x + -2x2 = x2 + ((10 * 8 + -1x * 8) + -1x * (10 + -1x)) 18x + -2x2 = x2 + ((80 + -8x) + -1x * (10 + -1x)) 18x + -2x2 = x2 + (80 + -8x + (10 * -1x + -1x * -1x)) 18x + -2x2 = x2 + (80 + -8x + (-10x + 1x2)) Combine like terms: -8x + -10x = -18x 18x + -2x2 = x2 + (80 + -18x + 1x2) Reorder the terms: 18x + -2x2 = 80 + -18x + x2 + 1x2 Combine like terms: x2 + 1x2 = 2x2 18x + -2x2 = 80 + -18x + 2x2 Solving 18x + -2x2 = 80 + -18x + 2x2 Solving for variable 'x'. Reorder the terms: -80 + 18x + 18x + -2x2 + -2x2 = 80 + -18x + 2x2 + -80 + 18x + -2x2 Combine like terms: 18x + 18x = 36x -80 + 36x + -2x2 + -2x2 = 80 + -18x + 2x2 + -80 + 18x + -2x2 Combine like terms: -2x2 + -2x2 = -4x2 -80 + 36x + -4x2 = 80 + -18x + 2x2 + -80 + 18x + -2x2 Reorder the terms: -80 + 36x + -4x2 = 80 + -80 + -18x + 18x + 2x2 + -2x2 Combine like terms: 80 + -80 = 0 -80 + 36x + -4x2 = 0 + -18x + 18x + 2x2 + -2x2 -80 + 36x + -4x2 = -18x + 18x + 2x2 + -2x2 Combine like terms: -18x + 18x = 0 -80 + 36x + -4x2 = 0 + 2x2 + -2x2 -80 + 36x + -4x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -80 + 36x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-20 + 9x + -1x2) = 0 Factor a trinomial. 4((-5 + x)(4 + -1x)) = 0 Ignore the factor 4.Subproblem 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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {5, 4}
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