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Simplifying x2 + 2x + -363 = 0 Reorder the terms: -363 + 2x + x2 = 0 Solving -363 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '363' to each side of the equation. -363 + 2x + 363 + x2 = 0 + 363 Reorder the terms: -363 + 363 + 2x + x2 = 0 + 363 Combine like terms: -363 + 363 = 0 0 + 2x + x2 = 0 + 363 2x + x2 = 0 + 363 Combine like terms: 0 + 363 = 363 2x + x2 = 363 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 = 363 + 1 Reorder the terms: 1 + 2x + x2 = 363 + 1 Combine like terms: 363 + 1 = 364 1 + 2x + x2 = 364 Factor a perfect square on the left side: (x + 1)(x + 1) = 364 Calculate the square root of the right side: 19.078784028 Break this problem into two subproblems by setting (x + 1) equal to 19.078784028 and -19.078784028.Subproblem 1
x + 1 = 19.078784028 Simplifying x + 1 = 19.078784028 Reorder the terms: 1 + x = 19.078784028 Solving 1 + x = 19.078784028 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 = 19.078784028 + -1 Combine like terms: 1 + -1 = 0 0 + x = 19.078784028 + -1 x = 19.078784028 + -1 Combine like terms: 19.078784028 + -1 = 18.078784028 x = 18.078784028 Simplifying x = 18.078784028Subproblem 2
x + 1 = -19.078784028 Simplifying x + 1 = -19.078784028 Reorder the terms: 1 + x = -19.078784028 Solving 1 + x = -19.078784028 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 = -19.078784028 + -1 Combine like terms: 1 + -1 = 0 0 + x = -19.078784028 + -1 x = -19.078784028 + -1 Combine like terms: -19.078784028 + -1 = -20.078784028 x = -20.078784028 Simplifying x = -20.078784028Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.078784028, -20.078784028}
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