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Simplifying 0 = 11x2 + -64x + 45 Reorder the terms: 0 = 45 + -64x + 11x2 Solving 0 = 45 + -64x + 11x2 Solving for variable 'x'. Combine like terms: 0 + -45 = -45 -45 + 64x + -11x2 = 45 + -64x + 11x2 + -45 + 64x + -11x2 Reorder the terms: -45 + 64x + -11x2 = 45 + -45 + -64x + 64x + 11x2 + -11x2 Combine like terms: 45 + -45 = 0 -45 + 64x + -11x2 = 0 + -64x + 64x + 11x2 + -11x2 -45 + 64x + -11x2 = -64x + 64x + 11x2 + -11x2 Combine like terms: -64x + 64x = 0 -45 + 64x + -11x2 = 0 + 11x2 + -11x2 -45 + 64x + -11x2 = 11x2 + -11x2 Combine like terms: 11x2 + -11x2 = 0 -45 + 64x + -11x2 = 0 Factor a trinomial. (-5 + x)(9 + -11x) = 0Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 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 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Subproblem 2
Set the factor '(9 + -11x)' equal to zero and attempt to solve: Simplifying 9 + -11x = 0 Solving 9 + -11x = 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 + -11x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -11x = 0 + -9 -11x = 0 + -9 Combine like terms: 0 + -9 = -9 -11x = -9 Divide each side by '-11'. x = 0.8181818182 Simplifying x = 0.8181818182Solution
x = {5, 0.8181818182}
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