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Simplifying 100 = -1x2 + 25x Reorder the terms: 100 = 25x + -1x2 Solving 100 = 25x + -1x2 Solving for variable 'x'. Reorder the terms: 100 + -25x + x2 = 25x + -25x + -1x2 + x2 Combine like terms: 25x + -25x = 0 100 + -25x + x2 = 0 + -1x2 + x2 100 + -25x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 100 + -25x + x2 = 0 Factor a trinomial. (5 + -1x)(20 + -1x) = 0Subproblem 1
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 = 5Subproblem 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 = {5, 20}
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