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Simplifying x2 + -2x + -378 = 0 Reorder the terms: -378 + -2x + x2 = 0 Solving -378 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '378' to each side of the equation. -378 + -2x + 378 + x2 = 0 + 378 Reorder the terms: -378 + 378 + -2x + x2 = 0 + 378 Combine like terms: -378 + 378 = 0 0 + -2x + x2 = 0 + 378 -2x + x2 = 0 + 378 Combine like terms: 0 + 378 = 378 -2x + x2 = 378 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 = 378 + 1 Reorder the terms: 1 + -2x + x2 = 378 + 1 Combine like terms: 378 + 1 = 379 1 + -2x + x2 = 379 Factor a perfect square on the left side: (x + -1)(x + -1) = 379 Calculate the square root of the right side: 19.467922334 Break this problem into two subproblems by setting (x + -1) equal to 19.467922334 and -19.467922334.Subproblem 1
x + -1 = 19.467922334 Simplifying x + -1 = 19.467922334 Reorder the terms: -1 + x = 19.467922334 Solving -1 + x = 19.467922334 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 = 19.467922334 + 1 Combine like terms: -1 + 1 = 0 0 + x = 19.467922334 + 1 x = 19.467922334 + 1 Combine like terms: 19.467922334 + 1 = 20.467922334 x = 20.467922334 Simplifying x = 20.467922334Subproblem 2
x + -1 = -19.467922334 Simplifying x + -1 = -19.467922334 Reorder the terms: -1 + x = -19.467922334 Solving -1 + x = -19.467922334 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 = -19.467922334 + 1 Combine like terms: -1 + 1 = 0 0 + x = -19.467922334 + 1 x = -19.467922334 + 1 Combine like terms: -19.467922334 + 1 = -18.467922334 x = -18.467922334 Simplifying x = -18.467922334Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.467922334, -18.467922334}
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