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Simplifying 2x2 + 17x = 6x + 6 Reorder the terms: 17x + 2x2 = 6x + 6 Reorder the terms: 17x + 2x2 = 6 + 6x Solving 17x + 2x2 = 6 + 6x Solving for variable 'x'. Reorder the terms: -6 + 17x + -6x + 2x2 = 6 + 6x + -6 + -6x Combine like terms: 17x + -6x = 11x -6 + 11x + 2x2 = 6 + 6x + -6 + -6x Reorder the terms: -6 + 11x + 2x2 = 6 + -6 + 6x + -6x Combine like terms: 6 + -6 = 0 -6 + 11x + 2x2 = 0 + 6x + -6x -6 + 11x + 2x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -6 + 11x + 2x2 = 0 Factor a trinomial. (-6 + -1x)(1 + -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 '(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 = 0.5Solution
x = {-6, 0.5}
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