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Simplifying X2 + 2X + -0.5 = 0 Reorder the terms: -0.5 + 2X + X2 = 0 Solving -0.5 + 2X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 2X + 0.5 + X2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 2X + X2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 2X + X2 = 0 + 0.5 2X + X2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 2X + X2 = 0.5 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 = 0.5 + 1 Reorder the terms: 1 + 2X + X2 = 0.5 + 1 Combine like terms: 0.5 + 1 = 1.5 1 + 2X + X2 = 1.5 Factor a perfect square on the left side: (X + 1)(X + 1) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (X + 1) equal to 1.224744871 and -1.224744871.Subproblem 1
X + 1 = 1.224744871 Simplifying X + 1 = 1.224744871 Reorder the terms: 1 + X = 1.224744871 Solving 1 + X = 1.224744871 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 = 1.224744871 + -1 Combine like terms: 1 + -1 = 0 0 + X = 1.224744871 + -1 X = 1.224744871 + -1 Combine like terms: 1.224744871 + -1 = 0.224744871 X = 0.224744871 Simplifying X = 0.224744871Subproblem 2
X + 1 = -1.224744871 Simplifying X + 1 = -1.224744871 Reorder the terms: 1 + X = -1.224744871 Solving 1 + X = -1.224744871 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 = -1.224744871 + -1 Combine like terms: 1 + -1 = 0 0 + X = -1.224744871 + -1 X = -1.224744871 + -1 Combine like terms: -1.224744871 + -1 = -2.224744871 X = -2.224744871 Simplifying X = -2.224744871Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.224744871, -2.224744871}
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