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Simplifying 6x + 100 = x2 + -20x + 100 Reorder the terms: 100 + 6x = x2 + -20x + 100 Reorder the terms: 100 + 6x = 100 + -20x + x2 Add '-100' to each side of the equation. 100 + -100 + 6x = 100 + -20x + -100 + x2 Combine like terms: 100 + -100 = 0 0 + 6x = 100 + -20x + -100 + x2 6x = 100 + -20x + -100 + x2 Reorder the terms: 6x = 100 + -100 + -20x + x2 Combine like terms: 100 + -100 = 0 6x = 0 + -20x + x2 6x = -20x + x2 Solving 6x = -20x + x2 Solving for variable 'x'. Combine like terms: 6x + 20x = 26x 26x + -1x2 = -20x + x2 + 20x + -1x2 Reorder the terms: 26x + -1x2 = -20x + 20x + x2 + -1x2 Combine like terms: -20x + 20x = 0 26x + -1x2 = 0 + x2 + -1x2 26x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 26x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(26 + -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 '(26 + -1x)' equal to zero and attempt to solve: Simplifying 26 + -1x = 0 Solving 26 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-26' to each side of the equation. 26 + -26 + -1x = 0 + -26 Combine like terms: 26 + -26 = 0 0 + -1x = 0 + -26 -1x = 0 + -26 Combine like terms: 0 + -26 = -26 -1x = -26 Divide each side by '-1'. x = 26 Simplifying x = 26Solution
x = {0, 26}
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