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Simplifying 4x2 + 3x = 3x2 + -4x + 18 Reorder the terms: 3x + 4x2 = 3x2 + -4x + 18 Reorder the terms: 3x + 4x2 = 18 + -4x + 3x2 Solving 3x + 4x2 = 18 + -4x + 3x2 Solving for variable 'x'. Reorder the terms: -18 + 3x + 4x + 4x2 + -3x2 = 18 + -4x + 3x2 + -18 + 4x + -3x2 Combine like terms: 3x + 4x = 7x -18 + 7x + 4x2 + -3x2 = 18 + -4x + 3x2 + -18 + 4x + -3x2 Combine like terms: 4x2 + -3x2 = 1x2 -18 + 7x + 1x2 = 18 + -4x + 3x2 + -18 + 4x + -3x2 Reorder the terms: -18 + 7x + 1x2 = 18 + -18 + -4x + 4x + 3x2 + -3x2 Combine like terms: 18 + -18 = 0 -18 + 7x + 1x2 = 0 + -4x + 4x + 3x2 + -3x2 -18 + 7x + 1x2 = -4x + 4x + 3x2 + -3x2 Combine like terms: -4x + 4x = 0 -18 + 7x + 1x2 = 0 + 3x2 + -3x2 -18 + 7x + 1x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -18 + 7x + 1x2 = 0 Factor a trinomial. (-9 + -1x)(2 + -1x) = 0Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9Subproblem 2
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 = 2Solution
x = {-9, 2}
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