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Simplifying x(x + 2) = 378 Reorder the terms: x(2 + x) = 378 (2 * x + x * x) = 378 (2x + x2) = 378 Solving 2x + x2 = 378 Solving for variable 'x'. Reorder the terms: -378 + 2x + x2 = 378 + -378 Combine like terms: 378 + -378 = 0 -378 + 2x + x2 = 0 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 = 18.467922334 x = 18.467922334 Simplifying x = 18.467922334Subproblem 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 = -20.467922334 x = -20.467922334 Simplifying x = -20.467922334Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.467922334, -20.467922334}
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