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Simplifying 0 = 16x2 + -27x + 11 Reorder the terms: 0 = 11 + -27x + 16x2 Solving 0 = 11 + -27x + 16x2 Solving for variable 'x'. Combine like terms: 0 + -11 = -11 -11 + 27x + -16x2 = 11 + -27x + 16x2 + -11 + 27x + -16x2 Reorder the terms: -11 + 27x + -16x2 = 11 + -11 + -27x + 27x + 16x2 + -16x2 Combine like terms: 11 + -11 = 0 -11 + 27x + -16x2 = 0 + -27x + 27x + 16x2 + -16x2 -11 + 27x + -16x2 = -27x + 27x + 16x2 + -16x2 Combine like terms: -27x + 27x = 0 -11 + 27x + -16x2 = 0 + 16x2 + -16x2 -11 + 27x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -11 + 27x + -16x2 = 0 Factor a trinomial. (-1 + x)(11 + -16x) = 0Subproblem 1
Set the factor '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Simplifying x = 1Subproblem 2
Set the factor '(11 + -16x)' equal to zero and attempt to solve: Simplifying 11 + -16x = 0 Solving 11 + -16x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -16x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -16x = 0 + -11 -16x = 0 + -11 Combine like terms: 0 + -11 = -11 -16x = -11 Divide each side by '-16'. x = 0.6875 Simplifying x = 0.6875Solution
x = {1, 0.6875}
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