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Simplifying (1 + 2x)(3 + -1x) + x2 = 9 Multiply (1 + 2x) * (3 + -1x) (1(3 + -1x) + 2x * (3 + -1x)) + x2 = 9 ((3 * 1 + -1x * 1) + 2x * (3 + -1x)) + x2 = 9 ((3 + -1x) + 2x * (3 + -1x)) + x2 = 9 (3 + -1x + (3 * 2x + -1x * 2x)) + x2 = 9 (3 + -1x + (6x + -2x2)) + x2 = 9 Combine like terms: -1x + 6x = 5x (3 + 5x + -2x2) + x2 = 9 Combine like terms: -2x2 + x2 = -1x2 3 + 5x + -1x2 = 9 Solving 3 + 5x + -1x2 = 9 Solving for variable 'x'. Reorder the terms: 3 + -9 + 5x + -1x2 = 9 + -9 Combine like terms: 3 + -9 = -6 -6 + 5x + -1x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -6 + 5x + -1x2 = 0 Factor a trinomial. (-3 + x)(2 + -1x) = 0Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3Subproblem 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 = {3, 2}
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