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Simplifying X(9X + 24) = 4X2 + -25X + 54 Reorder the terms: X(24 + 9X) = 4X2 + -25X + 54 (24 * X + 9X * X) = 4X2 + -25X + 54 (24X + 9X2) = 4X2 + -25X + 54 Reorder the terms: 24X + 9X2 = 54 + -25X + 4X2 Solving 24X + 9X2 = 54 + -25X + 4X2 Solving for variable 'X'. Reorder the terms: -54 + 24X + 25X + 9X2 + -4X2 = 54 + -25X + 4X2 + -54 + 25X + -4X2 Combine like terms: 24X + 25X = 49X -54 + 49X + 9X2 + -4X2 = 54 + -25X + 4X2 + -54 + 25X + -4X2 Combine like terms: 9X2 + -4X2 = 5X2 -54 + 49X + 5X2 = 54 + -25X + 4X2 + -54 + 25X + -4X2 Reorder the terms: -54 + 49X + 5X2 = 54 + -54 + -25X + 25X + 4X2 + -4X2 Combine like terms: 54 + -54 = 0 -54 + 49X + 5X2 = 0 + -25X + 25X + 4X2 + -4X2 -54 + 49X + 5X2 = -25X + 25X + 4X2 + -4X2 Combine like terms: -25X + 25X = 0 -54 + 49X + 5X2 = 0 + 4X2 + -4X2 -54 + 49X + 5X2 = 4X2 + -4X2 Combine like terms: 4X2 + -4X2 = 0 -54 + 49X + 5X2 = 0 Factor a trinomial. (-54 + -5X)(1 + -1X) = 0Subproblem 1
Set the factor '(-54 + -5X)' equal to zero and attempt to solve: Simplifying -54 + -5X = 0 Solving -54 + -5X = 0 Move all terms containing X to the left, all other terms to the right. Add '54' to each side of the equation. -54 + 54 + -5X = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -5X = 0 + 54 -5X = 0 + 54 Combine like terms: 0 + 54 = 54 -5X = 54 Divide each side by '-5'. X = -10.8 Simplifying X = -10.8Subproblem 2
Set the factor '(1 + -1X)' equal to zero and attempt to solve: Simplifying 1 + -1X = 0 Solving 1 + -1X = 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 + -1X = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1X = 0 + -1 -1X = 0 + -1 Combine like terms: 0 + -1 = -1 -1X = -1 Divide each side by '-1'. X = 1 Simplifying X = 1Solution
X = {-10.8, 1}
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