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Simplifying (10 + x)(70 + -1x) = 1600 Multiply (10 + x) * (70 + -1x) (10(70 + -1x) + x(70 + -1x)) = 1600 ((70 * 10 + -1x * 10) + x(70 + -1x)) = 1600 ((700 + -10x) + x(70 + -1x)) = 1600 (700 + -10x + (70 * x + -1x * x)) = 1600 (700 + -10x + (70x + -1x2)) = 1600 Combine like terms: -10x + 70x = 60x (700 + 60x + -1x2) = 1600 Solving 700 + 60x + -1x2 = 1600 Solving for variable 'x'. Reorder the terms: 700 + -1600 + 60x + -1x2 = 1600 + -1600 Combine like terms: 700 + -1600 = -900 -900 + 60x + -1x2 = 1600 + -1600 Combine like terms: 1600 + -1600 = 0 -900 + 60x + -1x2 = 0 Factor a trinomial. (-30 + x)(30 + -1x) = 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 '(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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