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Simplifying 400 + 1100x + -100x2 = 3200 Solving 400 + 1100x + -100x2 = 3200 Solving for variable 'x'. Reorder the terms: 400 + -3200 + 1100x + -100x2 = 3200 + -3200 Combine like terms: 400 + -3200 = -2800 -2800 + 1100x + -100x2 = 3200 + -3200 Combine like terms: 3200 + -3200 = 0 -2800 + 1100x + -100x2 = 0 Factor out the Greatest Common Factor (GCF), '100'. 100(-28 + 11x + -1x2) = 0 Factor a trinomial. 100((-7 + x)(4 + -1x)) = 0 Ignore the factor 100.Subproblem 1
Set the factor '(-7 + x)' equal to zero and attempt to solve: Simplifying -7 + x = 0 Solving -7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + x = 0 + 7 x = 0 + 7 Combine like terms: 0 + 7 = 7 x = 7 Simplifying x = 7Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {7, 4}
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