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Simplifying 0 = 3x2 + 7x + 2 Reorder the terms: 0 = 2 + 7x + 3x2 Solving 0 = 2 + 7x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -2 = -2 -2 + -7x + -3x2 = 2 + 7x + 3x2 + -2 + -7x + -3x2 Reorder the terms: -2 + -7x + -3x2 = 2 + -2 + 7x + -7x + 3x2 + -3x2 Combine like terms: 2 + -2 = 0 -2 + -7x + -3x2 = 0 + 7x + -7x + 3x2 + -3x2 -2 + -7x + -3x2 = 7x + -7x + 3x2 + -3x2 Combine like terms: 7x + -7x = 0 -2 + -7x + -3x2 = 0 + 3x2 + -3x2 -2 + -7x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -2 + -7x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 7x + 3x2) = 0 Factor a trinomial. -1((2 + x)(1 + 3x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 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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