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Simplifying x2 + x + -371 = 0 Reorder the terms: -371 + x + x2 = 0 Solving -371 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '371' to each side of the equation. -371 + x + 371 + x2 = 0 + 371 Reorder the terms: -371 + 371 + x + x2 = 0 + 371 Combine like terms: -371 + 371 = 0 0 + x + x2 = 0 + 371 x + x2 = 0 + 371 Combine like terms: 0 + 371 = 371 x + x2 = 371 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 = 371 + 0.25 Reorder the terms: 0.25 + x + x2 = 371 + 0.25 Combine like terms: 371 + 0.25 = 371.25 0.25 + x + x2 = 371.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 371.25 Calculate the square root of the right side: 19.267848868 Break this problem into two subproblems by setting (x + 0.5) equal to 19.267848868 and -19.267848868.Subproblem 1
x + 0.5 = 19.267848868 Simplifying x + 0.5 = 19.267848868 Reorder the terms: 0.5 + x = 19.267848868 Solving 0.5 + x = 19.267848868 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 = 19.267848868 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 19.267848868 + -0.5 x = 19.267848868 + -0.5 Combine like terms: 19.267848868 + -0.5 = 18.767848868 x = 18.767848868 Simplifying x = 18.767848868Subproblem 2
x + 0.5 = -19.267848868 Simplifying x + 0.5 = -19.267848868 Reorder the terms: 0.5 + x = -19.267848868 Solving 0.5 + x = -19.267848868 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 = -19.267848868 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -19.267848868 + -0.5 x = -19.267848868 + -0.5 Combine like terms: -19.267848868 + -0.5 = -19.767848868 x = -19.767848868 Simplifying x = -19.767848868Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.767848868, -19.767848868}
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