x^2-3.18x-15.53=0

Solution for x^2-3.18x-15.53=0 equation:

Simplifying
x2 + -3.18x + -15.53 = 0

Reorder the terms:
-15.53 + -3.18x + x2 = 0

Solving
-15.53 + -3.18x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '15.53' to each side of the equation.
-15.53 + -3.18x + 15.53 + x2 = 0 + 15.53

Reorder the terms:
-15.53 + 15.53 + -3.18x + x2 = 0 + 15.53

Combine like terms: -15.53 + 15.53 = 0.00
0.00 + -3.18x + x2 = 0 + 15.53
-3.18x + x2 = 0 + 15.53

Combine like terms: 0 + 15.53 = 15.53
-3.18x + x2 = 15.53

The x term is -3.18x.  Take half its coefficient (-1.59).
Square it (2.5281) and add it to both sides.

Add '2.5281' to each side of the equation.
-3.18x + 2.5281 + x2 = 15.53 + 2.5281

Reorder the terms:
2.5281 + -3.18x + x2 = 15.53 + 2.5281

Combine like terms: 15.53 + 2.5281 = 18.0581
2.5281 + -3.18x + x2 = 18.0581

Factor a perfect square on the left side:
(x + -1.59)(x + -1.59) = 18.0581

Calculate the square root of the right side: 4.249482321

Break this problem into two subproblems by setting 
(x + -1.59) equal to 4.249482321 and -4.249482321.

Subproblem 1
x + -1.59 = 4.249482321

Simplifying
x + -1.59 = 4.249482321

Reorder the terms:
-1.59 + x = 4.249482321

Solving
-1.59 + x = 4.249482321

Solving for variable 'x'.

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

Add '1.59' to each side of the equation.
-1.59 + 1.59 + x = 4.249482321 + 1.59

Combine like terms: -1.59 + 1.59 = 0.00
0.00 + x = 4.249482321 + 1.59
x = 4.249482321 + 1.59

Combine like terms: 4.249482321 + 1.59 = 5.839482321
x = 5.839482321

Simplifying
x = 5.839482321

Subproblem 2
x + -1.59 = -4.249482321

Simplifying
x + -1.59 = -4.249482321

Reorder the terms:
-1.59 + x = -4.249482321

Solving
-1.59 + x = -4.249482321

Solving for variable 'x'.

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

Add '1.59' to each side of the equation.
-1.59 + 1.59 + x = -4.249482321 + 1.59

Combine like terms: -1.59 + 1.59 = 0.00
0.00 + x = -4.249482321 + 1.59
x = -4.249482321 + 1.59

Combine like terms: -4.249482321 + 1.59 = -2.659482321
x = -2.659482321

Simplifying
x = -2.659482321

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.839482321, -2.659482321}