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Simplifying 13x2 + -5x = 6 + -12x2 Reorder the terms: -5x + 13x2 = 6 + -12x2 Solving -5x + 13x2 = 6 + -12x2 Solving for variable 'x'. Reorder the terms: -6 + -5x + 13x2 + 12x2 = 6 + -12x2 + -6 + 12x2 Combine like terms: 13x2 + 12x2 = 25x2 -6 + -5x + 25x2 = 6 + -12x2 + -6 + 12x2 Reorder the terms: -6 + -5x + 25x2 = 6 + -6 + -12x2 + 12x2 Combine like terms: 6 + -6 = 0 -6 + -5x + 25x2 = 0 + -12x2 + 12x2 -6 + -5x + 25x2 = -12x2 + 12x2 Combine like terms: -12x2 + 12x2 = 0 -6 + -5x + 25x2 = 0 Factor a trinomial. (-2 + -5x)(3 + -5x) = 0Subproblem 1
Set the factor '(-2 + -5x)' equal to zero and attempt to solve: Simplifying -2 + -5x = 0 Solving -2 + -5x = 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 + -5x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5x = 0 + 2 -5x = 0 + 2 Combine like terms: 0 + 2 = 2 -5x = 2 Divide each side by '-5'. x = -0.4 Simplifying x = -0.4Subproblem 2
Set the factor '(3 + -5x)' equal to zero and attempt to solve: Simplifying 3 + -5x = 0 Solving 3 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5x = 0 + -3 -5x = 0 + -3 Combine like terms: 0 + -3 = -3 -5x = -3 Divide each side by '-5'. x = 0.6 Simplifying x = 0.6Solution
x = {-0.4, 0.6}
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