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Simplifying 6x2 = 13x + -5 Reorder the terms: 6x2 = -5 + 13x Solving 6x2 = -5 + 13x Solving for variable 'x'. Reorder the terms: 5 + -13x + 6x2 = -5 + 13x + 5 + -13x Reorder the terms: 5 + -13x + 6x2 = -5 + 5 + 13x + -13x Combine like terms: -5 + 5 = 0 5 + -13x + 6x2 = 0 + 13x + -13x 5 + -13x + 6x2 = 13x + -13x Combine like terms: 13x + -13x = 0 5 + -13x + 6x2 = 0 Factor a trinomial. (1 + -2x)(5 + -3x) = 0Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve: Simplifying 5 + -3x = 0 Solving 5 + -3x = 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 + -3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x = 0 + -5 -3x = 0 + -5 Combine like terms: 0 + -5 = -5 -3x = -5 Divide each side by '-3'. x = 1.666666667 Simplifying x = 1.666666667Solution
x = {0.5, 1.666666667}
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