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Simplifying 2x2 + 13x = 6x + 30 Reorder the terms: 13x + 2x2 = 6x + 30 Reorder the terms: 13x + 2x2 = 30 + 6x Solving 13x + 2x2 = 30 + 6x Solving for variable 'x'. Reorder the terms: -30 + 13x + -6x + 2x2 = 30 + 6x + -30 + -6x Combine like terms: 13x + -6x = 7x -30 + 7x + 2x2 = 30 + 6x + -30 + -6x Reorder the terms: -30 + 7x + 2x2 = 30 + -30 + 6x + -6x Combine like terms: 30 + -30 = 0 -30 + 7x + 2x2 = 0 + 6x + -6x -30 + 7x + 2x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -30 + 7x + 2x2 = 0 Factor a trinomial. (-6 + -1x)(5 + -2x) = 0Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 2
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 = 2.5Solution
x = {-6, 2.5}
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