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Simplifying 0 = 380x + -10500 + -1x2 Reorder the terms: 0 = -10500 + 380x + -1x2 Solving 0 = -10500 + 380x + -1x2 Solving for variable 'x'. Combine like terms: 0 + 10500 = 10500 10500 + -380x + x2 = -10500 + 380x + -1x2 + 10500 + -380x + x2 Reorder the terms: 10500 + -380x + x2 = -10500 + 10500 + 380x + -380x + -1x2 + x2 Combine like terms: -10500 + 10500 = 0 10500 + -380x + x2 = 0 + 380x + -380x + -1x2 + x2 10500 + -380x + x2 = 380x + -380x + -1x2 + x2 Combine like terms: 380x + -380x = 0 10500 + -380x + x2 = 0 + -1x2 + x2 10500 + -380x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 10500 + -380x + x2 = 0 Factor a trinomial. (30 + -1x)(350 + -1x) = 0Subproblem 1
Set the factor '(30 + -1x)' equal to zero and attempt to solve: Simplifying 30 + -1x = 0 Solving 30 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + -1x = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -1x = 0 + -30 -1x = 0 + -30 Combine like terms: 0 + -30 = -30 -1x = -30 Divide each side by '-1'. x = 30 Simplifying x = 30Subproblem 2
Set the factor '(350 + -1x)' equal to zero and attempt to solve: Simplifying 350 + -1x = 0 Solving 350 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-350' to each side of the equation. 350 + -350 + -1x = 0 + -350 Combine like terms: 350 + -350 = 0 0 + -1x = 0 + -350 -1x = 0 + -350 Combine like terms: 0 + -350 = -350 -1x = -350 Divide each side by '-1'. x = 350 Simplifying x = 350Solution
x = {30, 350}
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