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Simplifying 2X(3X + 2) + -1 = 5X + 1 Reorder the terms: 2X(2 + 3X) + -1 = 5X + 1 (2 * 2X + 3X * 2X) + -1 = 5X + 1 (4X + 6X2) + -1 = 5X + 1 Reorder the terms: -1 + 4X + 6X2 = 5X + 1 Reorder the terms: -1 + 4X + 6X2 = 1 + 5X Solving -1 + 4X + 6X2 = 1 + 5X Solving for variable 'X'. Reorder the terms: -1 + -1 + 4X + -5X + 6X2 = 1 + 5X + -1 + -5X Combine like terms: -1 + -1 = -2 -2 + 4X + -5X + 6X2 = 1 + 5X + -1 + -5X Combine like terms: 4X + -5X = -1X -2 + -1X + 6X2 = 1 + 5X + -1 + -5X Reorder the terms: -2 + -1X + 6X2 = 1 + -1 + 5X + -5X Combine like terms: 1 + -1 = 0 -2 + -1X + 6X2 = 0 + 5X + -5X -2 + -1X + 6X2 = 5X + -5X Combine like terms: 5X + -5X = 0 -2 + -1X + 6X2 = 0 Factor a trinomial. (-1 + -2X)(2 + -3X) = 0Subproblem 1
Set the factor '(-1 + -2X)' equal to zero and attempt to solve: Simplifying -1 + -2X = 0 Solving -1 + -2X = 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 + -2X = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2X = 0 + 1 -2X = 0 + 1 Combine like terms: 0 + 1 = 1 -2X = 1 Divide each side by '-2'. X = -0.5 Simplifying X = -0.5Subproblem 2
Set the factor '(2 + -3X)' equal to zero and attempt to solve: Simplifying 2 + -3X = 0 Solving 2 + -3X = 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 + -3X = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3X = 0 + -2 -3X = 0 + -2 Combine like terms: 0 + -2 = -2 -3X = -2 Divide each side by '-3'. X = 0.6666666667 Simplifying X = 0.6666666667Solution
X = {-0.5, 0.6666666667}
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