5x^2-96x-344=0

Solution for 5x^2-96x-344=0 equation:

Simplifying
5x2 + -96x + -344 = 0

Reorder the terms:
-344 + -96x + 5x2 = 0

Solving
-344 + -96x + 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'.
-68.8 + -19.2x + x2 = 0

Move the constant term to the right:

Add '68.8' to each side of the equation.
-68.8 + -19.2x + 68.8 + x2 = 0 + 68.8

Reorder the terms:
-68.8 + 68.8 + -19.2x + x2 = 0 + 68.8

Combine like terms: -68.8 + 68.8 = 0.0
0.0 + -19.2x + x2 = 0 + 68.8
-19.2x + x2 = 0 + 68.8

Combine like terms: 0 + 68.8 = 68.8
-19.2x + x2 = 68.8

The x term is -19.2x.  Take half its coefficient (-9.6).
Square it (92.16) and add it to both sides.

Add '92.16' to each side of the equation.
-19.2x + 92.16 + x2 = 68.8 + 92.16

Reorder the terms:
92.16 + -19.2x + x2 = 68.8 + 92.16

Combine like terms: 68.8 + 92.16 = 160.96
92.16 + -19.2x + x2 = 160.96

Factor a perfect square on the left side:
(x + -9.6)(x + -9.6) = 160.96

Calculate the square root of the right side: 12.687001222

Break this problem into two subproblems by setting 
(x + -9.6) equal to 12.687001222 and -12.687001222.

Subproblem 1
x + -9.6 = 12.687001222

Simplifying
x + -9.6 = 12.687001222

Reorder the terms:
-9.6 + x = 12.687001222

Solving
-9.6 + x = 12.687001222

Solving for variable 'x'.

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

Add '9.6' to each side of the equation.
-9.6 + 9.6 + x = 12.687001222 + 9.6

Combine like terms: -9.6 + 9.6 = 0.0
0.0 + x = 12.687001222 + 9.6
x = 12.687001222 + 9.6

Combine like terms: 12.687001222 + 9.6 = 22.287001222
x = 22.287001222

Simplifying
x = 22.287001222

Subproblem 2
x + -9.6 = -12.687001222

Simplifying
x + -9.6 = -12.687001222

Reorder the terms:
-9.6 + x = -12.687001222

Solving
-9.6 + x = -12.687001222

Solving for variable 'x'.

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

Add '9.6' to each side of the equation.
-9.6 + 9.6 + x = -12.687001222 + 9.6

Combine like terms: -9.6 + 9.6 = 0.0
0.0 + x = -12.687001222 + 9.6
x = -12.687001222 + 9.6

Combine like terms: -12.687001222 + 9.6 = -3.087001222
x = -3.087001222

Simplifying
x = -3.087001222

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.287001222, -3.087001222}