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Simplifying 200x = 6300 + 40x + x2 Solving 200x = 6300 + 40x + x2 Solving for variable 'x'. Reorder the terms: -6300 + 200x + -40x + -1x2 = 6300 + 40x + x2 + -6300 + -40x + -1x2 Combine like terms: 200x + -40x = 160x -6300 + 160x + -1x2 = 6300 + 40x + x2 + -6300 + -40x + -1x2 Reorder the terms: -6300 + 160x + -1x2 = 6300 + -6300 + 40x + -40x + x2 + -1x2 Combine like terms: 6300 + -6300 = 0 -6300 + 160x + -1x2 = 0 + 40x + -40x + x2 + -1x2 -6300 + 160x + -1x2 = 40x + -40x + x2 + -1x2 Combine like terms: 40x + -40x = 0 -6300 + 160x + -1x2 = 0 + x2 + -1x2 -6300 + 160x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -6300 + 160x + -1x2 = 0 Factor a trinomial. (-90 + x)(70 + -1x) = 0Subproblem 1
Set the factor '(-90 + x)' equal to zero and attempt to solve: Simplifying -90 + x = 0 Solving -90 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = 0 + 90 Combine like terms: -90 + 90 = 0 0 + x = 0 + 90 x = 0 + 90 Combine like terms: 0 + 90 = 90 x = 90 Simplifying x = 90Subproblem 2
Set the factor '(70 + -1x)' equal to zero and attempt to solve: Simplifying 70 + -1x = 0 Solving 70 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-70' to each side of the equation. 70 + -70 + -1x = 0 + -70 Combine like terms: 70 + -70 = 0 0 + -1x = 0 + -70 -1x = 0 + -70 Combine like terms: 0 + -70 = -70 -1x = -70 Divide each side by '-1'. x = 70 Simplifying x = 70Solution
x = {90, 70}
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