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Simplifying X(9X + 24) = 4X2 + -15X + 54 Reorder the terms: X(24 + 9X) = 4X2 + -15X + 54 (24 * X + 9X * X) = 4X2 + -15X + 54 (24X + 9X2) = 4X2 + -15X + 54 Reorder the terms: 24X + 9X2 = 54 + -15X + 4X2 Solving 24X + 9X2 = 54 + -15X + 4X2 Solving for variable 'X'. Reorder the terms: -54 + 24X + 15X + 9X2 + -4X2 = 54 + -15X + 4X2 + -54 + 15X + -4X2 Combine like terms: 24X + 15X = 39X -54 + 39X + 9X2 + -4X2 = 54 + -15X + 4X2 + -54 + 15X + -4X2 Combine like terms: 9X2 + -4X2 = 5X2 -54 + 39X + 5X2 = 54 + -15X + 4X2 + -54 + 15X + -4X2 Reorder the terms: -54 + 39X + 5X2 = 54 + -54 + -15X + 15X + 4X2 + -4X2 Combine like terms: 54 + -54 = 0 -54 + 39X + 5X2 = 0 + -15X + 15X + 4X2 + -4X2 -54 + 39X + 5X2 = -15X + 15X + 4X2 + -4X2 Combine like terms: -15X + 15X = 0 -54 + 39X + 5X2 = 0 + 4X2 + -4X2 -54 + 39X + 5X2 = 4X2 + -4X2 Combine like terms: 4X2 + -4X2 = 0 -54 + 39X + 5X2 = 0 Factor a trinomial. (-9 + -1X)(6 + -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 '(6 + -5X)' equal to zero and attempt to solve: Simplifying 6 + -5X = 0 Solving 6 + -5X = 0 Move all terms containing X to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5X = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5X = 0 + -6 -5X = 0 + -6 Combine like terms: 0 + -6 = -6 -5X = -6 Divide each side by '-5'. X = 1.2 Simplifying X = 1.2Solution
X = {-9, 1.2}
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