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Simplifying -3x2 + 100x + 500 = 800 Reorder the terms: 500 + 100x + -3x2 = 800 Solving 500 + 100x + -3x2 = 800 Solving for variable 'x'. Reorder the terms: 500 + -800 + 100x + -3x2 = 800 + -800 Combine like terms: 500 + -800 = -300 -300 + 100x + -3x2 = 800 + -800 Combine like terms: 800 + -800 = 0 -300 + 100x + -3x2 = 0 Factor a trinomial. (-30 + x)(10 + -3x) = 0Subproblem 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 '(10 + -3x)' equal to zero and attempt to solve: Simplifying 10 + -3x = 0 Solving 10 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -3x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3x = 0 + -10 -3x = 0 + -10 Combine like terms: 0 + -10 = -10 -3x = -10 Divide each side by '-3'. x = 3.333333333 Simplifying x = 3.333333333Solution
x = {30, 3.333333333}
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