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Simplifying x2 + x + -398 = 0 Reorder the terms: -398 + x + x2 = 0 Solving -398 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '398' to each side of the equation. -398 + x + 398 + x2 = 0 + 398 Reorder the terms: -398 + 398 + x + x2 = 0 + 398 Combine like terms: -398 + 398 = 0 0 + x + x2 = 0 + 398 x + x2 = 0 + 398 Combine like terms: 0 + 398 = 398 x + x2 = 398 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. x + 0.25 + x2 = 398 + 0.25 Reorder the terms: 0.25 + x + x2 = 398 + 0.25 Combine like terms: 398 + 0.25 = 398.25 0.25 + x + x2 = 398.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 398.25 Calculate the square root of the right side: 19.956202043 Break this problem into two subproblems by setting (x + 0.5) equal to 19.956202043 and -19.956202043.Subproblem 1
x + 0.5 = 19.956202043 Simplifying x + 0.5 = 19.956202043 Reorder the terms: 0.5 + x = 19.956202043 Solving 0.5 + x = 19.956202043 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 = 19.956202043 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 19.956202043 + -0.5 x = 19.956202043 + -0.5 Combine like terms: 19.956202043 + -0.5 = 19.456202043 x = 19.456202043 Simplifying x = 19.456202043Subproblem 2
x + 0.5 = -19.956202043 Simplifying x + 0.5 = -19.956202043 Reorder the terms: 0.5 + x = -19.956202043 Solving 0.5 + x = -19.956202043 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 = -19.956202043 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -19.956202043 + -0.5 x = -19.956202043 + -0.5 Combine like terms: -19.956202043 + -0.5 = -20.456202043 x = -20.456202043 Simplifying x = -20.456202043Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.456202043, -20.456202043}
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