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Simplifying 13x2 + -1x + 5 = -2x2 + 11 Reorder the terms: 5 + -1x + 13x2 = -2x2 + 11 Reorder the terms: 5 + -1x + 13x2 = 11 + -2x2 Solving 5 + -1x + 13x2 = 11 + -2x2 Solving for variable 'x'. Reorder the terms: 5 + -11 + -1x + 13x2 + 2x2 = 11 + -2x2 + -11 + 2x2 Combine like terms: 5 + -11 = -6 -6 + -1x + 13x2 + 2x2 = 11 + -2x2 + -11 + 2x2 Combine like terms: 13x2 + 2x2 = 15x2 -6 + -1x + 15x2 = 11 + -2x2 + -11 + 2x2 Reorder the terms: -6 + -1x + 15x2 = 11 + -11 + -2x2 + 2x2 Combine like terms: 11 + -11 = 0 -6 + -1x + 15x2 = 0 + -2x2 + 2x2 -6 + -1x + 15x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -6 + -1x + 15x2 = 0 Factor a trinomial. (-3 + -5x)(2 + -3x) = 0Subproblem 1
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 = -0.6Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 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 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {-0.6, 0.6666666667}
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