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Simplifying 22 = (2x + 1)(3x + 1) Reorder the terms: 22 = (1 + 2x)(3x + 1) Reorder the terms: 22 = (1 + 2x)(1 + 3x) Multiply (1 + 2x) * (1 + 3x) 22 = (1(1 + 3x) + 2x * (1 + 3x)) 22 = ((1 * 1 + 3x * 1) + 2x * (1 + 3x)) 22 = ((1 + 3x) + 2x * (1 + 3x)) 22 = (1 + 3x + (1 * 2x + 3x * 2x)) 22 = (1 + 3x + (2x + 6x2)) Combine like terms: 3x + 2x = 5x 22 = (1 + 5x + 6x2) Solving 22 = 1 + 5x + 6x2 Solving for variable 'x'. Combine like terms: 22 + -1 = 21 21 + -5x + -6x2 = 1 + 5x + 6x2 + -1 + -5x + -6x2 Reorder the terms: 21 + -5x + -6x2 = 1 + -1 + 5x + -5x + 6x2 + -6x2 Combine like terms: 1 + -1 = 0 21 + -5x + -6x2 = 0 + 5x + -5x + 6x2 + -6x2 21 + -5x + -6x2 = 5x + -5x + 6x2 + -6x2 Combine like terms: 5x + -5x = 0 21 + -5x + -6x2 = 0 + 6x2 + -6x2 21 + -5x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 21 + -5x + -6x2 = 0 Factor a trinomial. (3 + -2x)(7 + 3x) = 0Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Subproblem 2
Set the factor '(7 + 3x)' equal to zero and attempt to solve: Simplifying 7 + 3x = 0 Solving 7 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3x = 0 + -7 3x = 0 + -7 Combine like terms: 0 + -7 = -7 3x = -7 Divide each side by '3'. x = -2.333333333 Simplifying x = -2.333333333Solution
x = {1.5, -2.333333333}
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