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Simplifying 2x2 + 18 = x2 + 11x Reorder the terms: 18 + 2x2 = x2 + 11x Reorder the terms: 18 + 2x2 = 11x + x2 Solving 18 + 2x2 = 11x + x2 Solving for variable 'x'. Reorder the terms: 18 + -11x + 2x2 + -1x2 = 11x + x2 + -11x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 18 + -11x + 1x2 = 11x + x2 + -11x + -1x2 Reorder the terms: 18 + -11x + 1x2 = 11x + -11x + x2 + -1x2 Combine like terms: 11x + -11x = 0 18 + -11x + 1x2 = 0 + x2 + -1x2 18 + -11x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 18 + -11x + 1x2 = 0 Factor a trinomial. (2 + -1x)(9 + -1x) = 0Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {2, 9}
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