x^2+2x-378=0

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Solution for x^2+2x-378=0 equation:


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 = 18.467922334 x = 18.467922334 Simplifying x = 18.467922334

Subproblem 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 = -20.467922334

Solution

The solution to the problem is based on the solutions from the subproblems. x = {18.467922334, -20.467922334}

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