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Simplifying 5x = -3x2 + 2 Reorder the terms: 5x = 2 + -3x2 Solving 5x = 2 + -3x2 Solving for variable 'x'. Reorder the terms: -2 + 5x + 3x2 = 2 + -3x2 + -2 + 3x2 Reorder the terms: -2 + 5x + 3x2 = 2 + -2 + -3x2 + 3x2 Combine like terms: 2 + -2 = 0 -2 + 5x + 3x2 = 0 + -3x2 + 3x2 -2 + 5x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -2 + 5x + 3x2 = 0 Factor a trinomial. (-2 + -1x)(1 + -3x) = 0Subproblem 1
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 = -2Subproblem 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 = {-2, 0.3333333333}
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