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Simplifying 2X2 + X = 0.44 Reorder the terms: X + 2X2 = 0.44 Solving X + 2X2 = 0.44 Solving for variable 'X'. Reorder the terms: -0.44 + X + 2X2 = 0.44 + -0.44 Combine like terms: 0.44 + -0.44 = 0.00 -0.44 + X + 2X2 = 0.00 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.22 + 0.5X + X2 = 0.00 Move the constant term to the right: Add '0.22' to each side of the equation. -0.22 + 0.5X + 0.22 + X2 = 0.00 + 0.22 Reorder the terms: -0.22 + 0.22 + 0.5X + X2 = 0.00 + 0.22 Combine like terms: -0.22 + 0.22 = 0.00 0.00 + 0.5X + X2 = 0.00 + 0.22 0.5X + X2 = 0.00 + 0.22 Combine like terms: 0.00 + 0.22 = 0.22 0.5X + X2 = 0.22 The X term is X. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5X + 0.25 + X2 = 0.22 + 0.25 Reorder the terms: 0.25 + 0.5X + X2 = 0.22 + 0.25 Combine like terms: 0.22 + 0.25 = 0.47 0.25 + 0.5X + X2 = 0.47 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 0.47 Calculate the square root of the right side: 0.68556546 Break this problem into two subproblems by setting (X + 0.5) equal to 0.68556546 and -0.68556546.Subproblem 1
X + 0.5 = 0.68556546 Simplifying X + 0.5 = 0.68556546 Reorder the terms: 0.5 + X = 0.68556546 Solving 0.5 + X = 0.68556546 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = 0.68556546 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 0.68556546 + -0.5 X = 0.68556546 + -0.5 Combine like terms: 0.68556546 + -0.5 = 0.18556546 X = 0.18556546 Simplifying X = 0.18556546Subproblem 2
X + 0.5 = -0.68556546 Simplifying X + 0.5 = -0.68556546 Reorder the terms: 0.5 + X = -0.68556546 Solving 0.5 + X = -0.68556546 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = -0.68556546 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -0.68556546 + -0.5 X = -0.68556546 + -0.5 Combine like terms: -0.68556546 + -0.5 = -1.18556546 X = -1.18556546 Simplifying X = -1.18556546Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.18556546, -1.18556546}
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