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Simplifying 11 = -16x2 + 16x + 8 Reorder the terms: 11 = 8 + 16x + -16x2 Solving 11 = 8 + 16x + -16x2 Solving for variable 'x'. Combine like terms: 11 + -8 = 3 3 + -16x + 16x2 = 8 + 16x + -16x2 + -8 + -16x + 16x2 Reorder the terms: 3 + -16x + 16x2 = 8 + -8 + 16x + -16x + -16x2 + 16x2 Combine like terms: 8 + -8 = 0 3 + -16x + 16x2 = 0 + 16x + -16x + -16x2 + 16x2 3 + -16x + 16x2 = 16x + -16x + -16x2 + 16x2 Combine like terms: 16x + -16x = 0 3 + -16x + 16x2 = 0 + -16x2 + 16x2 3 + -16x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 3 + -16x + 16x2 = 0 Factor a trinomial. (1 + -4x)(3 + -4x) = 0Subproblem 1
Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75Solution
x = {0.25, 0.75}
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