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Simplifying 1400 = 400 + 700x + -100x2 Solving 1400 = 400 + 700x + -100x2 Solving for variable 'x'. Combine like terms: 1400 + -400 = 1000 1000 + -700x + 100x2 = 400 + 700x + -100x2 + -400 + -700x + 100x2 Reorder the terms: 1000 + -700x + 100x2 = 400 + -400 + 700x + -700x + -100x2 + 100x2 Combine like terms: 400 + -400 = 0 1000 + -700x + 100x2 = 0 + 700x + -700x + -100x2 + 100x2 1000 + -700x + 100x2 = 700x + -700x + -100x2 + 100x2 Combine like terms: 700x + -700x = 0 1000 + -700x + 100x2 = 0 + -100x2 + 100x2 1000 + -700x + 100x2 = -100x2 + 100x2 Combine like terms: -100x2 + 100x2 = 0 1000 + -700x + 100x2 = 0 Factor out the Greatest Common Factor (GCF), '100'. 100(10 + -7x + x2) = 0 Factor a trinomial. 100((2 + -1x)(5 + -1x)) = 0 Ignore the factor 100.Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {2, 5}
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