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Simplifying x(9x + -11) = 4x2 + -28x + 54 Reorder the terms: x(-11 + 9x) = 4x2 + -28x + 54 (-11 * x + 9x * x) = 4x2 + -28x + 54 (-11x + 9x2) = 4x2 + -28x + 54 Reorder the terms: -11x + 9x2 = 54 + -28x + 4x2 Solving -11x + 9x2 = 54 + -28x + 4x2 Solving for variable 'x'. Reorder the terms: -54 + -11x + 28x + 9x2 + -4x2 = 54 + -28x + 4x2 + -54 + 28x + -4x2 Combine like terms: -11x + 28x = 17x -54 + 17x + 9x2 + -4x2 = 54 + -28x + 4x2 + -54 + 28x + -4x2 Combine like terms: 9x2 + -4x2 = 5x2 -54 + 17x + 5x2 = 54 + -28x + 4x2 + -54 + 28x + -4x2 Reorder the terms: -54 + 17x + 5x2 = 54 + -54 + -28x + 28x + 4x2 + -4x2 Combine like terms: 54 + -54 = 0 -54 + 17x + 5x2 = 0 + -28x + 28x + 4x2 + -4x2 -54 + 17x + 5x2 = -28x + 28x + 4x2 + -4x2 Combine like terms: -28x + 28x = 0 -54 + 17x + 5x2 = 0 + 4x2 + -4x2 -54 + 17x + 5x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -54 + 17x + 5x2 = 0 Factor a trinomial. (-27 + -5x)(2 + -1x) = 0Subproblem 1
Set the factor '(-27 + -5x)' equal to zero and attempt to solve: Simplifying -27 + -5x = 0 Solving -27 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + -5x = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -5x = 0 + 27 -5x = 0 + 27 Combine like terms: 0 + 27 = 27 -5x = 27 Divide each side by '-5'. x = -5.4 Simplifying x = -5.4Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-5.4, 2}
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