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Simplifying 10x2 + 3x + 2 = 5 + -2x2 + -2x Reorder the terms: 2 + 3x + 10x2 = 5 + -2x2 + -2x Reorder the terms: 2 + 3x + 10x2 = 5 + -2x + -2x2 Solving 2 + 3x + 10x2 = 5 + -2x + -2x2 Solving for variable 'x'. Reorder the terms: 2 + -5 + 3x + 2x + 10x2 + 2x2 = 5 + -2x + -2x2 + -5 + 2x + 2x2 Combine like terms: 2 + -5 = -3 -3 + 3x + 2x + 10x2 + 2x2 = 5 + -2x + -2x2 + -5 + 2x + 2x2 Combine like terms: 3x + 2x = 5x -3 + 5x + 10x2 + 2x2 = 5 + -2x + -2x2 + -5 + 2x + 2x2 Combine like terms: 10x2 + 2x2 = 12x2 -3 + 5x + 12x2 = 5 + -2x + -2x2 + -5 + 2x + 2x2 Reorder the terms: -3 + 5x + 12x2 = 5 + -5 + -2x + 2x + -2x2 + 2x2 Combine like terms: 5 + -5 = 0 -3 + 5x + 12x2 = 0 + -2x + 2x + -2x2 + 2x2 -3 + 5x + 12x2 = -2x + 2x + -2x2 + 2x2 Combine like terms: -2x + 2x = 0 -3 + 5x + 12x2 = 0 + -2x2 + 2x2 -3 + 5x + 12x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -3 + 5x + 12x2 = 0 Factor a trinomial. (-3 + -4x)(1 + -3x) = 0Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve: Simplifying -3 + -4x = 0 Solving -3 + -4x = 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 + -4x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4x = 0 + 3 -4x = 0 + 3 Combine like terms: 0 + 3 = 3 -4x = 3 Divide each side by '-4'. x = -0.75 Simplifying x = -0.75Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333Solution
x = {-0.75, 0.3333333333}
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