x^2-96x-80=0

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Solution for x^2-96x-80=0 equation: 


Simplifying
x2 + -96x + -80 = 0

Reorder the terms:
-80 + -96x + x2 = 0

Solving
-80 + -96x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + -96x + 80 + x2 = 0 + 80

Reorder the terms:
-80 + 80 + -96x + x2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + -96x + x2 = 0 + 80
-96x + x2 = 0 + 80

Combine like terms: 0 + 80 = 80
-96x + x2 = 80

The x term is -96x.  Take half its coefficient (-48).
Square it (2304) and add it to both sides.

Add '2304' to each side of the equation.
-96x + 2304 + x2 = 80 + 2304

Reorder the terms:
2304 + -96x + x2 = 80 + 2304

Combine like terms: 80 + 2304 = 2384
2304 + -96x + x2 = 2384

Factor a perfect square on the left side:
(x + -48)(x + -48) = 2384

Calculate the square root of the right side: 48.826222463

Break this problem into two subproblems by setting 
(x + -48) equal to 48.826222463 and -48.826222463.


Subproblem 1
x + -48 = 48.826222463

Simplifying
x + -48 = 48.826222463

Reorder the terms:
-48 + x = 48.826222463

Solving
-48 + x = 48.826222463

Solving for variable 'x'.

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

Add '48' to each side of the equation.
-48 + 48 + x = 48.826222463 + 48

Combine like terms: -48 + 48 = 0
0 + x = 48.826222463 + 48
x = 48.826222463 + 48

Combine like terms: 48.826222463 + 48 = 96.826222463
x = 96.826222463

Simplifying
x = 96.826222463


Subproblem 2
x + -48 = -48.826222463

Simplifying
x + -48 = -48.826222463

Reorder the terms:
-48 + x = -48.826222463

Solving
-48 + x = -48.826222463

Solving for variable 'x'.

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

Add '48' to each side of the equation.
-48 + 48 + x = -48.826222463 + 48

Combine like terms: -48 + 48 = 0
0 + x = -48.826222463 + 48
x = -48.826222463 + 48

Combine like terms: -48.826222463 + 48 = -0.826222463
x = -0.826222463

Simplifying
x = -0.826222463


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {96.826222463, -0.826222463}

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