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Simplifying 3(X + 1)(X + -2) = X(X + 2) Reorder the terms: 3(1 + X)(X + -2) = X(X + 2) Reorder the terms: 3(1 + X)(-2 + X) = X(X + 2) Multiply (1 + X) * (-2 + X) 3(1(-2 + X) + X(-2 + X)) = X(X + 2) 3((-2 * 1 + X * 1) + X(-2 + X)) = X(X + 2) 3((-2 + 1X) + X(-2 + X)) = X(X + 2) 3(-2 + 1X + (-2 * X + X * X)) = X(X + 2) 3(-2 + 1X + (-2X + X2)) = X(X + 2) Combine like terms: 1X + -2X = -1X 3(-2 + -1X + X2) = X(X + 2) (-2 * 3 + -1X * 3 + X2 * 3) = X(X + 2) (-6 + -3X + 3X2) = X(X + 2) Reorder the terms: -6 + -3X + 3X2 = X(2 + X) -6 + -3X + 3X2 = (2 * X + X * X) -6 + -3X + 3X2 = (2X + X2) Solving -6 + -3X + 3X2 = 2X + X2 Solving for variable 'X'. Reorder the terms: -6 + -3X + -2X + 3X2 + -1X2 = 2X + X2 + -2X + -1X2 Combine like terms: -3X + -2X = -5X -6 + -5X + 3X2 + -1X2 = 2X + X2 + -2X + -1X2 Combine like terms: 3X2 + -1X2 = 2X2 -6 + -5X + 2X2 = 2X + X2 + -2X + -1X2 Reorder the terms: -6 + -5X + 2X2 = 2X + -2X + X2 + -1X2 Combine like terms: 2X + -2X = 0 -6 + -5X + 2X2 = 0 + X2 + -1X2 -6 + -5X + 2X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 -6 + -5X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3 + -2.5X + X2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -2.5X + 3 + X2 = 0 + 3 Reorder the terms: -3 + 3 + -2.5X + X2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2.5X + X2 = 0 + 3 -2.5X + X2 = 0 + 3 Combine like terms: 0 + 3 = 3 -2.5X + X2 = 3 The X term is -2.5X. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5X + 1.5625 + X2 = 3 + 1.5625 Reorder the terms: 1.5625 + -2.5X + X2 = 3 + 1.5625 Combine like terms: 3 + 1.5625 = 4.5625 1.5625 + -2.5X + X2 = 4.5625 Factor a perfect square on the left side: (X + -1.25)(X + -1.25) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (X + -1.25) equal to 2.136000936 and -2.136000936.Subproblem 1
X + -1.25 = 2.136000936 Simplifying X + -1.25 = 2.136000936 Reorder the terms: -1.25 + X = 2.136000936 Solving -1.25 + X = 2.136000936 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + X = 2.136000936 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + X = 2.136000936 + 1.25 X = 2.136000936 + 1.25 Combine like terms: 2.136000936 + 1.25 = 3.386000936 X = 3.386000936 Simplifying X = 3.386000936Subproblem 2
X + -1.25 = -2.136000936 Simplifying X + -1.25 = -2.136000936 Reorder the terms: -1.25 + X = -2.136000936 Solving -1.25 + X = -2.136000936 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + X = -2.136000936 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + X = -2.136000936 + 1.25 X = -2.136000936 + 1.25 Combine like terms: -2.136000936 + 1.25 = -0.886000936 X = -0.886000936 Simplifying X = -0.886000936Solution
The solution to the problem is based on the solutions from the subproblems. X = {3.386000936, -0.886000936}
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