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Simplifying 120x + -2x2 = 1800 Solving 120x + -2x2 = 1800 Solving for variable 'x'. Reorder the terms: -1800 + 120x + -2x2 = 1800 + -1800 Combine like terms: 1800 + -1800 = 0 -1800 + 120x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-900 + 60x + -1x2) = 0 Factor a trinomial. 2((-30 + x)(30 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-30 + x)' equal to zero and attempt to solve: Simplifying -30 + x = 0 Solving -30 + x = 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 + x = 0 + 30 Combine like terms: -30 + 30 = 0 0 + x = 0 + 30 x = 0 + 30 Combine like terms: 0 + 30 = 30 x = 30 Simplifying x = 30Subproblem 2
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 = 30Solution
x = {30, 30}
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