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Simplifying x2 + 2x + -419 = 0 Reorder the terms: -419 + 2x + x2 = 0 Solving -419 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '419' to each side of the equation. -419 + 2x + 419 + x2 = 0 + 419 Reorder the terms: -419 + 419 + 2x + x2 = 0 + 419 Combine like terms: -419 + 419 = 0 0 + 2x + x2 = 0 + 419 2x + x2 = 0 + 419 Combine like terms: 0 + 419 = 419 2x + x2 = 419 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 = 419 + 1 Reorder the terms: 1 + 2x + x2 = 419 + 1 Combine like terms: 419 + 1 = 420 1 + 2x + x2 = 420 Factor a perfect square on the left side: (x + 1)(x + 1) = 420 Calculate the square root of the right side: 20.493901532 Break this problem into two subproblems by setting (x + 1) equal to 20.493901532 and -20.493901532.Subproblem 1
x + 1 = 20.493901532 Simplifying x + 1 = 20.493901532 Reorder the terms: 1 + x = 20.493901532 Solving 1 + x = 20.493901532 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 = 20.493901532 + -1 Combine like terms: 1 + -1 = 0 0 + x = 20.493901532 + -1 x = 20.493901532 + -1 Combine like terms: 20.493901532 + -1 = 19.493901532 x = 19.493901532 Simplifying x = 19.493901532Subproblem 2
x + 1 = -20.493901532 Simplifying x + 1 = -20.493901532 Reorder the terms: 1 + x = -20.493901532 Solving 1 + x = -20.493901532 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 = -20.493901532 + -1 Combine like terms: 1 + -1 = 0 0 + x = -20.493901532 + -1 x = -20.493901532 + -1 Combine like terms: -20.493901532 + -1 = -21.493901532 x = -21.493901532 Simplifying x = -21.493901532Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.493901532, -21.493901532}
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