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Simplifying 0 = 6x2 + -13x + -5 Reorder the terms: 0 = -5 + -13x + 6x2 Solving 0 = -5 + -13x + 6x2 Solving for variable 'x'. Combine like terms: 0 + 5 = 5 5 + 13x + -6x2 = -5 + -13x + 6x2 + 5 + 13x + -6x2 Reorder the terms: 5 + 13x + -6x2 = -5 + 5 + -13x + 13x + 6x2 + -6x2 Combine like terms: -5 + 5 = 0 5 + 13x + -6x2 = 0 + -13x + 13x + 6x2 + -6x2 5 + 13x + -6x2 = -13x + 13x + 6x2 + -6x2 Combine like terms: -13x + 13x = 0 5 + 13x + -6x2 = 0 + 6x2 + -6x2 5 + 13x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 5 + 13x + -6x2 = 0 Factor a trinomial. (5 + -2x)(1 + 3x) = 0Subproblem 1
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Subproblem 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 = {2.5, -0.3333333333}
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