x^2+54x-12=0

Solution for x^2+54x-12=0 equation:

Simplifying
x2 + 54x + -12 = 0

Reorder the terms:
-12 + 54x + x2 = 0

Solving
-12 + 54x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 54x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 54x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 54x + x2 = 0 + 12
54x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
54x + x2 = 12

The x term is 54x.  Take half its coefficient (27).
Square it (729) and add it to both sides.

Add '729' to each side of the equation.
54x + 729 + x2 = 12 + 729

Reorder the terms:
729 + 54x + x2 = 12 + 729

Combine like terms: 12 + 729 = 741
729 + 54x + x2 = 741

Factor a perfect square on the left side:
(x + 27)(x + 27) = 741

Calculate the square root of the right side: 27.221315178

Break this problem into two subproblems by setting 
(x + 27) equal to 27.221315178 and -27.221315178.

Subproblem 1
x + 27 = 27.221315178

Simplifying
x + 27 = 27.221315178

Reorder the terms:
27 + x = 27.221315178

Solving
27 + x = 27.221315178

Solving for variable 'x'.

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

Add '-27' to each side of the equation.
27 + -27 + x = 27.221315178 + -27

Combine like terms: 27 + -27 = 0
0 + x = 27.221315178 + -27
x = 27.221315178 + -27

Combine like terms: 27.221315178 + -27 = 0.221315178
x = 0.221315178

Simplifying
x = 0.221315178

Subproblem 2
x + 27 = -27.221315178

Simplifying
x + 27 = -27.221315178

Reorder the terms:
27 + x = -27.221315178

Solving
27 + x = -27.221315178

Solving for variable 'x'.

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

Add '-27' to each side of the equation.
27 + -27 + x = -27.221315178 + -27

Combine like terms: 27 + -27 = 0
0 + x = -27.221315178 + -27
x = -27.221315178 + -27

Combine like terms: -27.221315178 + -27 = -54.221315178
x = -54.221315178

Simplifying
x = -54.221315178

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.221315178, -54.221315178}