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Simplifying x2 + 2x + -388 = 0 Reorder the terms: -388 + 2x + x2 = 0 Solving -388 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '388' to each side of the equation. -388 + 2x + 388 + x2 = 0 + 388 Reorder the terms: -388 + 388 + 2x + x2 = 0 + 388 Combine like terms: -388 + 388 = 0 0 + 2x + x2 = 0 + 388 2x + x2 = 0 + 388 Combine like terms: 0 + 388 = 388 2x + x2 = 388 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 = 388 + 1 Reorder the terms: 1 + 2x + x2 = 388 + 1 Combine like terms: 388 + 1 = 389 1 + 2x + x2 = 389 Factor a perfect square on the left side: (x + 1)(x + 1) = 389 Calculate the square root of the right side: 19.723082923 Break this problem into two subproblems by setting (x + 1) equal to 19.723082923 and -19.723082923.Subproblem 1
x + 1 = 19.723082923 Simplifying x + 1 = 19.723082923 Reorder the terms: 1 + x = 19.723082923 Solving 1 + x = 19.723082923 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 = 19.723082923 + -1 Combine like terms: 1 + -1 = 0 0 + x = 19.723082923 + -1 x = 19.723082923 + -1 Combine like terms: 19.723082923 + -1 = 18.723082923 x = 18.723082923 Simplifying x = 18.723082923Subproblem 2
x + 1 = -19.723082923 Simplifying x + 1 = -19.723082923 Reorder the terms: 1 + x = -19.723082923 Solving 1 + x = -19.723082923 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 = -19.723082923 + -1 Combine like terms: 1 + -1 = 0 0 + x = -19.723082923 + -1 x = -19.723082923 + -1 Combine like terms: -19.723082923 + -1 = -20.723082923 x = -20.723082923 Simplifying x = -20.723082923Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.723082923, -20.723082923}
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