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Simplifying 100 = (10 + -1X)(10 + -1X) Multiply (10 + -1X) * (10 + -1X) 100 = (10(10 + -1X) + -1X * (10 + -1X)) 100 = ((10 * 10 + -1X * 10) + -1X * (10 + -1X)) 100 = ((100 + -10X) + -1X * (10 + -1X)) 100 = (100 + -10X + (10 * -1X + -1X * -1X)) 100 = (100 + -10X + (-10X + 1X2)) Combine like terms: -10X + -10X = -20X 100 = (100 + -20X + 1X2) Add '-100' to each side of the equation. 100 + -100 = 100 + -20X + -100 + 1X2 Combine like terms: 100 + -100 = 0 0 = 100 + -20X + -100 + 1X2 Reorder the terms: 0 = 100 + -100 + -20X + 1X2 Combine like terms: 100 + -100 = 0 0 = 0 + -20X + 1X2 0 = -20X + 1X2 Solving 0 = -20X + 1X2 Solving for variable 'X'. Remove the zero: 20X + -1X2 = -20X + 1X2 + 20X + -1X2 Reorder the terms: 20X + -1X2 = -20X + 20X + 1X2 + -1X2 Combine like terms: -20X + 20X = 0 20X + -1X2 = 0 + 1X2 + -1X2 20X + -1X2 = 1X2 + -1X2 Combine like terms: 1X2 + -1X2 = 0 20X + -1X2 = 0 Factor out the Greatest Common Factor (GCF), 'X'. X(20 + -1X) = 0Subproblem 1
Set the factor 'X' equal to zero and attempt to solve: Simplifying X = 0 Solving X = 0 Move all terms containing X to the left, all other terms to the right. Simplifying X = 0Subproblem 2
Set the factor '(20 + -1X)' equal to zero and attempt to solve: Simplifying 20 + -1X = 0 Solving 20 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1X = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1X = 0 + -20 -1X = 0 + -20 Combine like terms: 0 + -20 = -20 -1X = -20 Divide each side by '-1'. X = 20 Simplifying X = 20Solution
X = {0, 20}
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