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Simplifying 12x2 + 11x + 12 = 10x2 + 22x Reorder the terms: 12 + 11x + 12x2 = 10x2 + 22x Reorder the terms: 12 + 11x + 12x2 = 22x + 10x2 Solving 12 + 11x + 12x2 = 22x + 10x2 Solving for variable 'x'. Reorder the terms: 12 + 11x + -22x + 12x2 + -10x2 = 22x + 10x2 + -22x + -10x2 Combine like terms: 11x + -22x = -11x 12 + -11x + 12x2 + -10x2 = 22x + 10x2 + -22x + -10x2 Combine like terms: 12x2 + -10x2 = 2x2 12 + -11x + 2x2 = 22x + 10x2 + -22x + -10x2 Reorder the terms: 12 + -11x + 2x2 = 22x + -22x + 10x2 + -10x2 Combine like terms: 22x + -22x = 0 12 + -11x + 2x2 = 0 + 10x2 + -10x2 12 + -11x + 2x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 12 + -11x + 2x2 = 0 Factor a trinomial. (3 + -2x)(4 + -1x) = 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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {1.5, 4}
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