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Simplifying 580x = 12000 + 7x2 Solving 580x = 12000 + 7x2 Solving for variable 'x'. Reorder the terms: -12000 + 580x + -7x2 = 12000 + 7x2 + -12000 + -7x2 Reorder the terms: -12000 + 580x + -7x2 = 12000 + -12000 + 7x2 + -7x2 Combine like terms: 12000 + -12000 = 0 -12000 + 580x + -7x2 = 0 + 7x2 + -7x2 -12000 + 580x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 -12000 + 580x + -7x2 = 0 Factor a trinomial. (-300 + 7x)(40 + -1x) = 0Subproblem 1
Set the factor '(-300 + 7x)' equal to zero and attempt to solve: Simplifying -300 + 7x = 0 Solving -300 + 7x = 0 Move all terms containing x to the left, all other terms to the right. Add '300' to each side of the equation. -300 + 300 + 7x = 0 + 300 Combine like terms: -300 + 300 = 0 0 + 7x = 0 + 300 7x = 0 + 300 Combine like terms: 0 + 300 = 300 7x = 300 Divide each side by '7'. x = 42.85714286 Simplifying x = 42.85714286Subproblem 2
Set the factor '(40 + -1x)' equal to zero and attempt to solve: Simplifying 40 + -1x = 0 Solving 40 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + -1x = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -1x = 0 + -40 -1x = 0 + -40 Combine like terms: 0 + -40 = -40 -1x = -40 Divide each side by '-1'. x = 40 Simplifying x = 40Solution
x = {42.85714286, 40}
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