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Simplifying 2500 = -1x2 + 40x + 2100 Reorder the terms: 2500 = 2100 + 40x + -1x2 Solving 2500 = 2100 + 40x + -1x2 Solving for variable 'x'. Combine like terms: 2500 + -2100 = 400 400 + -40x + x2 = 2100 + 40x + -1x2 + -2100 + -40x + x2 Reorder the terms: 400 + -40x + x2 = 2100 + -2100 + 40x + -40x + -1x2 + x2 Combine like terms: 2100 + -2100 = 0 400 + -40x + x2 = 0 + 40x + -40x + -1x2 + x2 400 + -40x + x2 = 40x + -40x + -1x2 + x2 Combine like terms: 40x + -40x = 0 400 + -40x + x2 = 0 + -1x2 + x2 400 + -40x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 400 + -40x + x2 = 0 Factor a trinomial. (20 + -1x)(20 + -1x) = 0Subproblem 1
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 = 20Subproblem 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 = {20, 20}
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