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Simplifying 0 = 3x2 + -13x + 4 Reorder the terms: 0 = 4 + -13x + 3x2 Solving 0 = 4 + -13x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + 13x + -3x2 = 4 + -13x + 3x2 + -4 + 13x + -3x2 Reorder the terms: -4 + 13x + -3x2 = 4 + -4 + -13x + 13x + 3x2 + -3x2 Combine like terms: 4 + -4 = 0 -4 + 13x + -3x2 = 0 + -13x + 13x + 3x2 + -3x2 -4 + 13x + -3x2 = -13x + 13x + 3x2 + -3x2 Combine like terms: -13x + 13x = 0 -4 + 13x + -3x2 = 0 + 3x2 + -3x2 -4 + 13x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -4 + 13x + -3x2 = 0 Factor a trinomial. (-4 + x)(1 + -3x) = 0Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 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 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Simplifying x = 4Subproblem 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 = {4, 0.3333333333}
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