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Simplifying x(112 + -2x) = 1368 (112 * x + -2x * x) = 1368 (112x + -2x2) = 1368 Solving 112x + -2x2 = 1368 Solving for variable 'x'. Reorder the terms: -1368 + 112x + -2x2 = 1368 + -1368 Combine like terms: 1368 + -1368 = 0 -1368 + 112x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-684 + 56x + -1x2) = 0 Factor a trinomial. 2((-38 + x)(18 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-38 + x)' equal to zero and attempt to solve: Simplifying -38 + x = 0 Solving -38 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '38' to each side of the equation. -38 + 38 + x = 0 + 38 Combine like terms: -38 + 38 = 0 0 + x = 0 + 38 x = 0 + 38 Combine like terms: 0 + 38 = 38 x = 38 Simplifying x = 38Subproblem 2
Set the factor '(18 + -1x)' equal to zero and attempt to solve: Simplifying 18 + -1x = 0 Solving 18 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + -1x = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -1x = 0 + -18 -1x = 0 + -18 Combine like terms: 0 + -18 = -18 -1x = -18 Divide each side by '-1'. x = 18 Simplifying x = 18Solution
x = {38, 18}
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