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Simplifying 0 = -1x2 + 100x + -2500 Reorder the terms: 0 = -2500 + 100x + -1x2 Solving 0 = -2500 + 100x + -1x2 Solving for variable 'x'. Combine like terms: 0 + 2500 = 2500 2500 + -100x + x2 = -2500 + 100x + -1x2 + 2500 + -100x + x2 Reorder the terms: 2500 + -100x + x2 = -2500 + 2500 + 100x + -100x + -1x2 + x2 Combine like terms: -2500 + 2500 = 0 2500 + -100x + x2 = 0 + 100x + -100x + -1x2 + x2 2500 + -100x + x2 = 100x + -100x + -1x2 + x2 Combine like terms: 100x + -100x = 0 2500 + -100x + x2 = 0 + -1x2 + x2 2500 + -100x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 2500 + -100x + x2 = 0 Factor a trinomial. (50 + -1x)(50 + -1x) = 0Subproblem 1
Set the factor '(50 + -1x)' equal to zero and attempt to solve: Simplifying 50 + -1x = 0 Solving 50 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + -1x = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -1x = 0 + -50 -1x = 0 + -50 Combine like terms: 0 + -50 = -50 -1x = -50 Divide each side by '-1'. x = 50 Simplifying x = 50Subproblem 2
Set the factor '(50 + -1x)' equal to zero and attempt to solve: Simplifying 50 + -1x = 0 Solving 50 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + -1x = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -1x = 0 + -50 -1x = 0 + -50 Combine like terms: 0 + -50 = -50 -1x = -50 Divide each side by '-1'. x = 50 Simplifying x = 50Solution
x = {50, 50}
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