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Simplifying X(9X + 1) = 4X2 + -23X + 36 Reorder the terms: X(1 + 9X) = 4X2 + -23X + 36 (1 * X + 9X * X) = 4X2 + -23X + 36 (1X + 9X2) = 4X2 + -23X + 36 Reorder the terms: 1X + 9X2 = 36 + -23X + 4X2 Solving 1X + 9X2 = 36 + -23X + 4X2 Solving for variable 'X'. Reorder the terms: -36 + 1X + 23X + 9X2 + -4X2 = 36 + -23X + 4X2 + -36 + 23X + -4X2 Combine like terms: 1X + 23X = 24X -36 + 24X + 9X2 + -4X2 = 36 + -23X + 4X2 + -36 + 23X + -4X2 Combine like terms: 9X2 + -4X2 = 5X2 -36 + 24X + 5X2 = 36 + -23X + 4X2 + -36 + 23X + -4X2 Reorder the terms: -36 + 24X + 5X2 = 36 + -36 + -23X + 23X + 4X2 + -4X2 Combine like terms: 36 + -36 = 0 -36 + 24X + 5X2 = 0 + -23X + 23X + 4X2 + -4X2 -36 + 24X + 5X2 = -23X + 23X + 4X2 + -4X2 Combine like terms: -23X + 23X = 0 -36 + 24X + 5X2 = 0 + 4X2 + -4X2 -36 + 24X + 5X2 = 4X2 + -4X2 Combine like terms: 4X2 + -4X2 = 0 -36 + 24X + 5X2 = 0 Factor a trinomial. (-6 + -1X)(6 + -5X) = 0Subproblem 1
Set the factor '(-6 + -1X)' equal to zero and attempt to solve: Simplifying -6 + -1X = 0 Solving -6 + -1X = 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 + -1X = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1X = 0 + 6 -1X = 0 + 6 Combine like terms: 0 + 6 = 6 -1X = 6 Divide each side by '-1'. X = -6 Simplifying X = -6Subproblem 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 = {-6, 1.2}
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