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Simplifying x(8x + 11) = 3x2 + -25x + 81 Reorder the terms: x(11 + 8x) = 3x2 + -25x + 81 (11 * x + 8x * x) = 3x2 + -25x + 81 (11x + 8x2) = 3x2 + -25x + 81 Reorder the terms: 11x + 8x2 = 81 + -25x + 3x2 Solving 11x + 8x2 = 81 + -25x + 3x2 Solving for variable 'x'. Reorder the terms: -81 + 11x + 25x + 8x2 + -3x2 = 81 + -25x + 3x2 + -81 + 25x + -3x2 Combine like terms: 11x + 25x = 36x -81 + 36x + 8x2 + -3x2 = 81 + -25x + 3x2 + -81 + 25x + -3x2 Combine like terms: 8x2 + -3x2 = 5x2 -81 + 36x + 5x2 = 81 + -25x + 3x2 + -81 + 25x + -3x2 Reorder the terms: -81 + 36x + 5x2 = 81 + -81 + -25x + 25x + 3x2 + -3x2 Combine like terms: 81 + -81 = 0 -81 + 36x + 5x2 = 0 + -25x + 25x + 3x2 + -3x2 -81 + 36x + 5x2 = -25x + 25x + 3x2 + -3x2 Combine like terms: -25x + 25x = 0 -81 + 36x + 5x2 = 0 + 3x2 + -3x2 -81 + 36x + 5x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -81 + 36x + 5x2 = 0 Factor a trinomial. (-9 + -1x)(9 + -5x) = 0Subproblem 1
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 = -9Subproblem 2
Set the factor '(9 + -5x)' equal to zero and attempt to solve: Simplifying 9 + -5x = 0 Solving 9 + -5x = 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 + -5x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -5x = 0 + -9 -5x = 0 + -9 Combine like terms: 0 + -9 = -9 -5x = -9 Divide each side by '-5'. x = 1.8 Simplifying x = 1.8Solution
x = {-9, 1.8}
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