x^2+13.89x=2400

Solution for x^2+13.89x=2400 equation:

Simplifying
x2 + 13.89x = 2400

Reorder the terms:
13.89x + x2 = 2400

Solving
13.89x + x2 = 2400

Solving for variable 'x'.

Reorder the terms:
-2400 + 13.89x + x2 = 2400 + -2400

Combine like terms: 2400 + -2400 = 0
-2400 + 13.89x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2400' to each side of the equation.
-2400 + 13.89x + 2400 + x2 = 0 + 2400

Reorder the terms:
-2400 + 2400 + 13.89x + x2 = 0 + 2400

Combine like terms: -2400 + 2400 = 0
0 + 13.89x + x2 = 0 + 2400
13.89x + x2 = 0 + 2400

Combine like terms: 0 + 2400 = 2400
13.89x + x2 = 2400

The x term is 13.89x.  Take half its coefficient (6.945).
Square it (48.233025) and add it to both sides.

Add '48.233025' to each side of the equation.
13.89x + 48.233025 + x2 = 2400 + 48.233025

Reorder the terms:
48.233025 + 13.89x + x2 = 2400 + 48.233025

Combine like terms: 2400 + 48.233025 = 2448.233025
48.233025 + 13.89x + x2 = 2448.233025

Factor a perfect square on the left side:
(x + 6.945)(x + 6.945) = 2448.233025

Calculate the square root of the right side: 49.479622321

Break this problem into two subproblems by setting 
(x + 6.945) equal to 49.479622321 and -49.479622321.

Subproblem 1
x + 6.945 = 49.479622321

Simplifying
x + 6.945 = 49.479622321

Reorder the terms:
6.945 + x = 49.479622321

Solving
6.945 + x = 49.479622321

Solving for variable 'x'.

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

Add '-6.945' to each side of the equation.
6.945 + -6.945 + x = 49.479622321 + -6.945

Combine like terms: 6.945 + -6.945 = 0.000
0.000 + x = 49.479622321 + -6.945
x = 49.479622321 + -6.945

Combine like terms: 49.479622321 + -6.945 = 42.534622321
x = 42.534622321

Simplifying
x = 42.534622321

Subproblem 2
x + 6.945 = -49.479622321

Simplifying
x + 6.945 = -49.479622321

Reorder the terms:
6.945 + x = -49.479622321

Solving
6.945 + x = -49.479622321

Solving for variable 'x'.

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

Add '-6.945' to each side of the equation.
6.945 + -6.945 + x = -49.479622321 + -6.945

Combine like terms: 6.945 + -6.945 = 0.000
0.000 + x = -49.479622321 + -6.945
x = -49.479622321 + -6.945

Combine like terms: -49.479622321 + -6.945 = -56.424622321
x = -56.424622321

Simplifying
x = -56.424622321

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {42.534622321, -56.424622321}