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Simplifying x(9x + 4) = 4x2 + -38x + 27 Reorder the terms: x(4 + 9x) = 4x2 + -38x + 27 (4 * x + 9x * x) = 4x2 + -38x + 27 (4x + 9x2) = 4x2 + -38x + 27 Reorder the terms: 4x + 9x2 = 27 + -38x + 4x2 Solving 4x + 9x2 = 27 + -38x + 4x2 Solving for variable 'x'. Reorder the terms: -27 + 4x + 38x + 9x2 + -4x2 = 27 + -38x + 4x2 + -27 + 38x + -4x2 Combine like terms: 4x + 38x = 42x -27 + 42x + 9x2 + -4x2 = 27 + -38x + 4x2 + -27 + 38x + -4x2 Combine like terms: 9x2 + -4x2 = 5x2 -27 + 42x + 5x2 = 27 + -38x + 4x2 + -27 + 38x + -4x2 Reorder the terms: -27 + 42x + 5x2 = 27 + -27 + -38x + 38x + 4x2 + -4x2 Combine like terms: 27 + -27 = 0 -27 + 42x + 5x2 = 0 + -38x + 38x + 4x2 + -4x2 -27 + 42x + 5x2 = -38x + 38x + 4x2 + -4x2 Combine like terms: -38x + 38x = 0 -27 + 42x + 5x2 = 0 + 4x2 + -4x2 -27 + 42x + 5x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -27 + 42x + 5x2 = 0 Factor a trinomial. (-9 + -1x)(3 + -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 '(3 + -5x)' equal to zero and attempt to solve: Simplifying 3 + -5x = 0 Solving 3 + -5x = 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 + -5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5x = 0 + -3 -5x = 0 + -3 Combine like terms: 0 + -3 = -3 -5x = -3 Divide each side by '-5'. x = 0.6 Simplifying x = 0.6Solution
x = {-9, 0.6}
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