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Simplifying 2X * X + 8X + -1 = 0 Multiply X * X 2X2 + 8X + -1 = 0 Reorder the terms: -1 + 8X + 2X2 = 0 Solving -1 + 8X + 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'. -0.5 + 4X + X2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 4X + 0.5 + X2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 4X + X2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 4X + X2 = 0 + 0.5 4X + X2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 4X + X2 = 0.5 The X term is 4X. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4X + 4 + X2 = 0.5 + 4 Reorder the terms: 4 + 4X + X2 = 0.5 + 4 Combine like terms: 0.5 + 4 = 4.5 4 + 4X + X2 = 4.5 Factor a perfect square on the left side: (X + 2)(X + 2) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (X + 2) equal to 2.121320344 and -2.121320344.Subproblem 1
X + 2 = 2.121320344 Simplifying X + 2 = 2.121320344 Reorder the terms: 2 + X = 2.121320344 Solving 2 + X = 2.121320344 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = 2.121320344 + -2 Combine like terms: 2 + -2 = 0 0 + X = 2.121320344 + -2 X = 2.121320344 + -2 Combine like terms: 2.121320344 + -2 = 0.121320344 X = 0.121320344 Simplifying X = 0.121320344Subproblem 2
X + 2 = -2.121320344 Simplifying X + 2 = -2.121320344 Reorder the terms: 2 + X = -2.121320344 Solving 2 + X = -2.121320344 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = -2.121320344 + -2 Combine like terms: 2 + -2 = 0 0 + X = -2.121320344 + -2 X = -2.121320344 + -2 Combine like terms: -2.121320344 + -2 = -4.121320344 X = -4.121320344 Simplifying X = -4.121320344Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.121320344, -4.121320344}
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