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Simplifying 11x(x + -1) = -9x2 + 3 Reorder the terms: 11x(-1 + x) = -9x2 + 3 (-1 * 11x + x * 11x) = -9x2 + 3 (-11x + 11x2) = -9x2 + 3 Reorder the terms: -11x + 11x2 = 3 + -9x2 Solving -11x + 11x2 = 3 + -9x2 Solving for variable 'x'. Reorder the terms: -3 + -11x + 11x2 + 9x2 = 3 + -9x2 + -3 + 9x2 Combine like terms: 11x2 + 9x2 = 20x2 -3 + -11x + 20x2 = 3 + -9x2 + -3 + 9x2 Reorder the terms: -3 + -11x + 20x2 = 3 + -3 + -9x2 + 9x2 Combine like terms: 3 + -3 = 0 -3 + -11x + 20x2 = 0 + -9x2 + 9x2 -3 + -11x + 20x2 = -9x2 + 9x2 Combine like terms: -9x2 + 9x2 = 0 -3 + -11x + 20x2 = 0 Factor a trinomial. (-1 + -5x)(3 + -4x) = 0Subproblem 1
Set the factor '(-1 + -5x)' equal to zero and attempt to solve: Simplifying -1 + -5x = 0 Solving -1 + -5x = 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 + -5x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5x = 0 + 1 -5x = 0 + 1 Combine like terms: 0 + 1 = 1 -5x = 1 Divide each side by '-5'. x = -0.2 Simplifying x = -0.2Subproblem 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 = {-0.2, 0.75}
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