x^2+9x-396=0

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Solution for x^2+9x-396=0 equation: 


Simplifying
x2 + 9x + -396 = 0

Reorder the terms:
-396 + 9x + x2 = 0

Solving
-396 + 9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '396' to each side of the equation.
-396 + 9x + 396 + x2 = 0 + 396

Reorder the terms:
-396 + 396 + 9x + x2 = 0 + 396

Combine like terms: -396 + 396 = 0
0 + 9x + x2 = 0 + 396
9x + x2 = 0 + 396

Combine like terms: 0 + 396 = 396
9x + x2 = 396

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 396 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 396 + 20.25

Combine like terms: 396 + 20.25 = 416.25
20.25 + 9x + x2 = 416.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 416.25

Calculate the square root of the right side: 20.402205763

Break this problem into two subproblems by setting 
(x + 4.5) equal to 20.402205763 and -20.402205763.


Subproblem 1
x + 4.5 = 20.402205763

Simplifying
x + 4.5 = 20.402205763

Reorder the terms:
4.5 + x = 20.402205763

Solving
4.5 + x = 20.402205763

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 20.402205763 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 20.402205763 + -4.5
x = 20.402205763 + -4.5

Combine like terms: 20.402205763 + -4.5 = 15.902205763
x = 15.902205763

Simplifying
x = 15.902205763


Subproblem 2
x + 4.5 = -20.402205763

Simplifying
x + 4.5 = -20.402205763

Reorder the terms:
4.5 + x = -20.402205763

Solving
4.5 + x = -20.402205763

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -20.402205763 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -20.402205763 + -4.5
x = -20.402205763 + -4.5

Combine like terms: -20.402205763 + -4.5 = -24.902205763
x = -24.902205763

Simplifying
x = -24.902205763


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.902205763, -24.902205763}

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