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Simplifying (2X + -1)(X + -3) = 4 Reorder the terms: (-1 + 2X)(X + -3) = 4 Reorder the terms: (-1 + 2X)(-3 + X) = 4 Multiply (-1 + 2X) * (-3 + X) (-1(-3 + X) + 2X * (-3 + X)) = 4 ((-3 * -1 + X * -1) + 2X * (-3 + X)) = 4 ((3 + -1X) + 2X * (-3 + X)) = 4 (3 + -1X + (-3 * 2X + X * 2X)) = 4 (3 + -1X + (-6X + 2X2)) = 4 Combine like terms: -1X + -6X = -7X (3 + -7X + 2X2) = 4 Solving 3 + -7X + 2X2 = 4 Solving for variable 'X'. Reorder the terms: 3 + -4 + -7X + 2X2 = 4 + -4 Combine like terms: 3 + -4 = -1 -1 + -7X + 2X2 = 4 + -4 Combine like terms: 4 + -4 = 0 -1 + -7X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -3.5X + X2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -3.5X + 0.5 + X2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -3.5X + X2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -3.5X + X2 = 0 + 0.5 -3.5X + X2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -3.5X + X2 = 0.5 The X term is -3.5X. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5X + 3.0625 + X2 = 0.5 + 3.0625 Reorder the terms: 3.0625 + -3.5X + X2 = 0.5 + 3.0625 Combine like terms: 0.5 + 3.0625 = 3.5625 3.0625 + -3.5X + X2 = 3.5625 Factor a perfect square on the left side: (X + -1.75)(X + -1.75) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (X + -1.75) equal to 1.887458609 and -1.887458609.Subproblem 1
X + -1.75 = 1.887458609 Simplifying X + -1.75 = 1.887458609 Reorder the terms: -1.75 + X = 1.887458609 Solving -1.75 + X = 1.887458609 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + X = 1.887458609 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + X = 1.887458609 + 1.75 X = 1.887458609 + 1.75 Combine like terms: 1.887458609 + 1.75 = 3.637458609 X = 3.637458609 Simplifying X = 3.637458609Subproblem 2
X + -1.75 = -1.887458609 Simplifying X + -1.75 = -1.887458609 Reorder the terms: -1.75 + X = -1.887458609 Solving -1.75 + X = -1.887458609 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + X = -1.887458609 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + X = -1.887458609 + 1.75 X = -1.887458609 + 1.75 Combine like terms: -1.887458609 + 1.75 = -0.137458609 X = -0.137458609 Simplifying X = -0.137458609Solution
The solution to the problem is based on the solutions from the subproblems. X = {3.637458609, -0.137458609}
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