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Simplifying 2x^{2}= 11x + 40 Reorder the terms: 2x^{2}= 40 + 11x Solving 2x^{2}= 40 + 11x Solving for variable 'x'. Reorder the terms: -40 + -11x + 2x^{2}= 40 + 11x + -40 + -11x Reorder the terms: -40 + -11x + 2x^{2}= 40 + -40 + 11x + -11x Combine like terms: 40 + -40 = 0 -40 + -11x + 2x^{2}= 0 + 11x + -11x -40 + -11x + 2x^{2}= 11x + -11x Combine like terms: 11x + -11x = 0 -40 + -11x + 2x^{2}= 0 Factor a trinomial. (-5 + -2x)(8 + -1x) = 0## Subproblem 1

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 = -2.5## Subproblem 2

Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8## Solution

x = {-2.5, 8}

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