5x^2-108x-441=0

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Solution for 5x^2-108x-441=0 equation: 


Simplifying
5x2 + -108x + -441 = 0

Reorder the terms:
-441 + -108x + 5x2 = 0

Solving
-441 + -108x + 5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-88.2 + -21.6x + x2 = 0

Move the constant term to the right:

Add '88.2' to each side of the equation.
-88.2 + -21.6x + 88.2 + x2 = 0 + 88.2

Reorder the terms:
-88.2 + 88.2 + -21.6x + x2 = 0 + 88.2

Combine like terms: -88.2 + 88.2 = 0.0
0.0 + -21.6x + x2 = 0 + 88.2
-21.6x + x2 = 0 + 88.2

Combine like terms: 0 + 88.2 = 88.2
-21.6x + x2 = 88.2

The x term is -21.6x.  Take half its coefficient (-10.8).
Square it (116.64) and add it to both sides.

Add '116.64' to each side of the equation.
-21.6x + 116.64 + x2 = 88.2 + 116.64

Reorder the terms:
116.64 + -21.6x + x2 = 88.2 + 116.64

Combine like terms: 88.2 + 116.64 = 204.84
116.64 + -21.6x + x2 = 204.84

Factor a perfect square on the left side:
(x + -10.8)(x + -10.8) = 204.84

Calculate the square root of the right side: 14.31223253

Break this problem into two subproblems by setting 
(x + -10.8) equal to 14.31223253 and -14.31223253.


Subproblem 1
x + -10.8 = 14.31223253

Simplifying
x + -10.8 = 14.31223253

Reorder the terms:
-10.8 + x = 14.31223253

Solving
-10.8 + x = 14.31223253

Solving for variable 'x'.

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

Add '10.8' to each side of the equation.
-10.8 + 10.8 + x = 14.31223253 + 10.8

Combine like terms: -10.8 + 10.8 = 0.0
0.0 + x = 14.31223253 + 10.8
x = 14.31223253 + 10.8

Combine like terms: 14.31223253 + 10.8 = 25.11223253
x = 25.11223253

Simplifying
x = 25.11223253


Subproblem 2
x + -10.8 = -14.31223253

Simplifying
x + -10.8 = -14.31223253

Reorder the terms:
-10.8 + x = -14.31223253

Solving
-10.8 + x = -14.31223253

Solving for variable 'x'.

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

Add '10.8' to each side of the equation.
-10.8 + 10.8 + x = -14.31223253 + 10.8

Combine like terms: -10.8 + 10.8 = 0.0
0.0 + x = -14.31223253 + 10.8
x = -14.31223253 + 10.8

Combine like terms: -14.31223253 + 10.8 = -3.51223253
x = -3.51223253

Simplifying
x = -3.51223253


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {25.11223253, -3.51223253}

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