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Simplifying 4x2 + 39x + 90 = 684 Reorder the terms: 90 + 39x + 4x2 = 684 Solving 90 + 39x + 4x2 = 684 Solving for variable 'x'. Reorder the terms: 90 + -684 + 39x + 4x2 = 684 + -684 Combine like terms: 90 + -684 = -594 -594 + 39x + 4x2 = 684 + -684 Combine like terms: 684 + -684 = 0 -594 + 39x + 4x2 = 0 Factor a trinomial. (-18 + -1x)(33 + -4x) = 0Subproblem 1
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 = -18Subproblem 2
Set the factor '(33 + -4x)' equal to zero and attempt to solve: Simplifying 33 + -4x = 0 Solving 33 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-33' to each side of the equation. 33 + -33 + -4x = 0 + -33 Combine like terms: 33 + -33 = 0 0 + -4x = 0 + -33 -4x = 0 + -33 Combine like terms: 0 + -33 = -33 -4x = -33 Divide each side by '-4'. x = 8.25 Simplifying x = 8.25Solution
x = {-18, 8.25}
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