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Simplifying 2X2 + 4X + -11 = 0 Reorder the terms: -11 + 4X + 2X2 = 0 Solving -11 + 4X + 2X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.5 + 2X + X2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 2X + 5.5 + X2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 2X + X2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 2X + X2 = 0 + 5.5 2X + X2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 2X + X2 = 5.5 The X term is 2X. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2X + 1 + X2 = 5.5 + 1 Reorder the terms: 1 + 2X + X2 = 5.5 + 1 Combine like terms: 5.5 + 1 = 6.5 1 + 2X + X2 = 6.5 Factor a perfect square on the left side: (X + 1)(X + 1) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (X + 1) equal to 2.549509757 and -2.549509757.Subproblem 1
X + 1 = 2.549509757 Simplifying X + 1 = 2.549509757 Reorder the terms: 1 + X = 2.549509757 Solving 1 + X = 2.549509757 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + X = 2.549509757 + -1 Combine like terms: 1 + -1 = 0 0 + X = 2.549509757 + -1 X = 2.549509757 + -1 Combine like terms: 2.549509757 + -1 = 1.549509757 X = 1.549509757 Simplifying X = 1.549509757Subproblem 2
X + 1 = -2.549509757 Simplifying X + 1 = -2.549509757 Reorder the terms: 1 + X = -2.549509757 Solving 1 + X = -2.549509757 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + X = -2.549509757 + -1 Combine like terms: 1 + -1 = 0 0 + X = -2.549509757 + -1 X = -2.549509757 + -1 Combine like terms: -2.549509757 + -1 = -3.549509757 X = -3.549509757 Simplifying X = -3.549509757Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.549509757, -3.549509757}
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