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Simplifying 2X(X + -4) = 4X + 1 Reorder the terms: 2X(-4 + X) = 4X + 1 (-4 * 2X + X * 2X) = 4X + 1 (-8X + 2X2) = 4X + 1 Reorder the terms: -8X + 2X2 = 1 + 4X Solving -8X + 2X2 = 1 + 4X Solving for variable 'X'. Reorder the terms: -1 + -8X + -4X + 2X2 = 1 + 4X + -1 + -4X Combine like terms: -8X + -4X = -12X -1 + -12X + 2X2 = 1 + 4X + -1 + -4X Reorder the terms: -1 + -12X + 2X2 = 1 + -1 + 4X + -4X Combine like terms: 1 + -1 = 0 -1 + -12X + 2X2 = 0 + 4X + -4X -1 + -12X + 2X2 = 4X + -4X Combine like terms: 4X + -4X = 0 -1 + -12X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -6X + X2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -6X + 0.5 + X2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -6X + X2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -6X + X2 = 0 + 0.5 -6X + X2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -6X + X2 = 0.5 The X term is -6X. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6X + 9 + X2 = 0.5 + 9 Reorder the terms: 9 + -6X + X2 = 0.5 + 9 Combine like terms: 0.5 + 9 = 9.5 9 + -6X + X2 = 9.5 Factor a perfect square on the left side: (X + -3)(X + -3) = 9.5 Calculate the square root of the right side: 3.082207001 Break this problem into two subproblems by setting (X + -3) equal to 3.082207001 and -3.082207001.Subproblem 1
X + -3 = 3.082207001 Simplifying X + -3 = 3.082207001 Reorder the terms: -3 + X = 3.082207001 Solving -3 + X = 3.082207001 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + X = 3.082207001 + 3 Combine like terms: -3 + 3 = 0 0 + X = 3.082207001 + 3 X = 3.082207001 + 3 Combine like terms: 3.082207001 + 3 = 6.082207001 X = 6.082207001 Simplifying X = 6.082207001Subproblem 2
X + -3 = -3.082207001 Simplifying X + -3 = -3.082207001 Reorder the terms: -3 + X = -3.082207001 Solving -3 + X = -3.082207001 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + X = -3.082207001 + 3 Combine like terms: -3 + 3 = 0 0 + X = -3.082207001 + 3 X = -3.082207001 + 3 Combine like terms: -3.082207001 + 3 = -0.082207001 X = -0.082207001 Simplifying X = -0.082207001Solution
The solution to the problem is based on the solutions from the subproblems. X = {6.082207001, -0.082207001}
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