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Simplifying 0 = 2(3x2 + -7x + 2) Reorder the terms: 0 = 2(2 + -7x + 3x2) 0 = (2 * 2 + -7x * 2 + 3x2 * 2) 0 = (4 + -14x + 6x2) Solving 0 = 4 + -14x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + 14x + -6x2 = 4 + -14x + 6x2 + -4 + 14x + -6x2 Reorder the terms: -4 + 14x + -6x2 = 4 + -4 + -14x + 14x + 6x2 + -6x2 Combine like terms: 4 + -4 = 0 -4 + 14x + -6x2 = 0 + -14x + 14x + 6x2 + -6x2 -4 + 14x + -6x2 = -14x + 14x + 6x2 + -6x2 Combine like terms: -14x + 14x = 0 -4 + 14x + -6x2 = 0 + 6x2 + -6x2 -4 + 14x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -4 + 14x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 7x + -3x2) = 0 Factor a trinomial. 2((-2 + x)(1 + -3x)) = 0 Ignore the factor 2.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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