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Simplifying 2x2 + 13x + -5 = 5 + -1x2 Reorder the terms: -5 + 13x + 2x2 = 5 + -1x2 Solving -5 + 13x + 2x2 = 5 + -1x2 Solving for variable 'x'. Reorder the terms: -5 + -5 + 13x + 2x2 + x2 = 5 + -1x2 + -5 + x2 Combine like terms: -5 + -5 = -10 -10 + 13x + 2x2 + x2 = 5 + -1x2 + -5 + x2 Combine like terms: 2x2 + x2 = 3x2 -10 + 13x + 3x2 = 5 + -1x2 + -5 + x2 Reorder the terms: -10 + 13x + 3x2 = 5 + -5 + -1x2 + x2 Combine like terms: 5 + -5 = 0 -10 + 13x + 3x2 = 0 + -1x2 + x2 -10 + 13x + 3x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -10 + 13x + 3x2 = 0 Factor a trinomial. (-5 + -1x)(2 + -3x) = 0Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 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 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 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 = {-5, 0.6666666667}
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