x^2-32x-196=0

Solution for x^2-32x-196=0 equation:

Simplifying
x2 + -32x + -196 = 0

Reorder the terms:
-196 + -32x + x2 = 0

Solving
-196 + -32x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '196' to each side of the equation.
-196 + -32x + 196 + x2 = 0 + 196

Reorder the terms:
-196 + 196 + -32x + x2 = 0 + 196

Combine like terms: -196 + 196 = 0
0 + -32x + x2 = 0 + 196
-32x + x2 = 0 + 196

Combine like terms: 0 + 196 = 196
-32x + x2 = 196

The x term is -32x.  Take half its coefficient (-16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
-32x + 256 + x2 = 196 + 256

Reorder the terms:
256 + -32x + x2 = 196 + 256

Combine like terms: 196 + 256 = 452
256 + -32x + x2 = 452

Factor a perfect square on the left side:
(x + -16)(x + -16) = 452

Calculate the square root of the right side: 21.260291625

Break this problem into two subproblems by setting 
(x + -16) equal to 21.260291625 and -21.260291625.

Subproblem 1
x + -16 = 21.260291625

Simplifying
x + -16 = 21.260291625

Reorder the terms:
-16 + x = 21.260291625

Solving
-16 + x = 21.260291625

Solving for variable 'x'.

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

Add '16' to each side of the equation.
-16 + 16 + x = 21.260291625 + 16

Combine like terms: -16 + 16 = 0
0 + x = 21.260291625 + 16
x = 21.260291625 + 16

Combine like terms: 21.260291625 + 16 = 37.260291625
x = 37.260291625

Simplifying
x = 37.260291625

Subproblem 2
x + -16 = -21.260291625

Simplifying
x + -16 = -21.260291625

Reorder the terms:
-16 + x = -21.260291625

Solving
-16 + x = -21.260291625

Solving for variable 'x'.

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

Add '16' to each side of the equation.
-16 + 16 + x = -21.260291625 + 16

Combine like terms: -16 + 16 = 0
0 + x = -21.260291625 + 16
x = -21.260291625 + 16

Combine like terms: -21.260291625 + 16 = -5.260291625
x = -5.260291625

Simplifying
x = -5.260291625

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {37.260291625, -5.260291625}