x^2+13.05x-16.5=0

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Solution for x^2+13.05x-16.5=0 equation: 


Simplifying
x2 + 13.05x + -16.5 = 0

Reorder the terms:
-16.5 + 13.05x + x2 = 0

Solving
-16.5 + 13.05x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '16.5' to each side of the equation.
-16.5 + 13.05x + 16.5 + x2 = 0 + 16.5

Reorder the terms:
-16.5 + 16.5 + 13.05x + x2 = 0 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + 13.05x + x2 = 0 + 16.5
13.05x + x2 = 0 + 16.5

Combine like terms: 0 + 16.5 = 16.5
13.05x + x2 = 16.5

The x term is 13.05x.  Take half its coefficient (6.525).
Square it (42.575625) and add it to both sides.

Add '42.575625' to each side of the equation.
13.05x + 42.575625 + x2 = 16.5 + 42.575625

Reorder the terms:
42.575625 + 13.05x + x2 = 16.5 + 42.575625

Combine like terms: 16.5 + 42.575625 = 59.075625
42.575625 + 13.05x + x2 = 59.075625

Factor a perfect square on the left side:
(x + 6.525)(x + 6.525) = 59.075625

Calculate the square root of the right side: 7.68606694

Break this problem into two subproblems by setting 
(x + 6.525) equal to 7.68606694 and -7.68606694.


Subproblem 1
x + 6.525 = 7.68606694

Simplifying
x + 6.525 = 7.68606694

Reorder the terms:
6.525 + x = 7.68606694

Solving
6.525 + x = 7.68606694

Solving for variable 'x'.

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

Add '-6.525' to each side of the equation.
6.525 + -6.525 + x = 7.68606694 + -6.525

Combine like terms: 6.525 + -6.525 = 0.000
0.000 + x = 7.68606694 + -6.525
x = 7.68606694 + -6.525

Combine like terms: 7.68606694 + -6.525 = 1.16106694
x = 1.16106694

Simplifying
x = 1.16106694


Subproblem 2
x + 6.525 = -7.68606694

Simplifying
x + 6.525 = -7.68606694

Reorder the terms:
6.525 + x = -7.68606694

Solving
6.525 + x = -7.68606694

Solving for variable 'x'.

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

Add '-6.525' to each side of the equation.
6.525 + -6.525 + x = -7.68606694 + -6.525

Combine like terms: 6.525 + -6.525 = 0.000
0.000 + x = -7.68606694 + -6.525
x = -7.68606694 + -6.525

Combine like terms: -7.68606694 + -6.525 = -14.21106694
x = -14.21106694

Simplifying
x = -14.21106694


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.16106694, -14.21106694}

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