x^2+12x=398

Solution for x^2+12x=398 equation:

Simplifying
x2 + 12x = 398

Reorder the terms:
12x + x2 = 398

Solving
12x + x2 = 398

Solving for variable 'x'.

Reorder the terms:
-398 + 12x + x2 = 398 + -398

Combine like terms: 398 + -398 = 0
-398 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '398' to each side of the equation.
-398 + 12x + 398 + x2 = 0 + 398

Reorder the terms:
-398 + 398 + 12x + x2 = 0 + 398

Combine like terms: -398 + 398 = 0
0 + 12x + x2 = 0 + 398
12x + x2 = 0 + 398

Combine like terms: 0 + 398 = 398
12x + x2 = 398

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 398 + 36

Reorder the terms:
36 + 12x + x2 = 398 + 36

Combine like terms: 398 + 36 = 434
36 + 12x + x2 = 434

Factor a perfect square on the left side:
(x + 6)(x + 6) = 434

Calculate the square root of the right side: 20.832666656

Break this problem into two subproblems by setting 
(x + 6) equal to 20.832666656 and -20.832666656.

Subproblem 1
x + 6 = 20.832666656

Simplifying
x + 6 = 20.832666656

Reorder the terms:
6 + x = 20.832666656

Solving
6 + x = 20.832666656

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + x = 20.832666656 + -6

Combine like terms: 6 + -6 = 0
0 + x = 20.832666656 + -6
x = 20.832666656 + -6

Combine like terms: 20.832666656 + -6 = 14.832666656
x = 14.832666656

Simplifying
x = 14.832666656

Subproblem 2
x + 6 = -20.832666656

Simplifying
x + 6 = -20.832666656

Reorder the terms:
6 + x = -20.832666656

Solving
6 + x = -20.832666656

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + x = -20.832666656 + -6

Combine like terms: 6 + -6 = 0
0 + x = -20.832666656 + -6
x = -20.832666656 + -6

Combine like terms: -20.832666656 + -6 = -26.832666656
x = -26.832666656

Simplifying
x = -26.832666656

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.832666656, -26.832666656}