5x^2-80x-485=0

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Solution for 5x^2-80x-485=0 equation: 


Simplifying
5x2 + -80x + -485 = 0

Reorder the terms:
-485 + -80x + 5x2 = 0

Solving
-485 + -80x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-97 + -16x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-97 + -16x + x2)' equal to zero and attempt to solve:

Simplifying
-97 + -16x + x2 = 0

Solving
-97 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '97' to each side of the equation.
-97 + -16x + 97 + x2 = 0 + 97

Reorder the terms:
-97 + 97 + -16x + x2 = 0 + 97

Combine like terms: -97 + 97 = 0
0 + -16x + x2 = 0 + 97
-16x + x2 = 0 + 97

Combine like terms: 0 + 97 = 97
-16x + x2 = 97

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = 97 + 64

Reorder the terms:
64 + -16x + x2 = 97 + 64

Combine like terms: 97 + 64 = 161
64 + -16x + x2 = 161

Factor a perfect square on the left side:
(x + -8)(x + -8) = 161

Calculate the square root of the right side: 12.68857754

Break this problem into two subproblems by setting 
(x + -8) equal to 12.68857754 and -12.68857754.


Subproblem 1
x + -8 = 12.68857754

Simplifying
x + -8 = 12.68857754

Reorder the terms:
-8 + x = 12.68857754

Solving
-8 + x = 12.68857754

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = 12.68857754 + 8

Combine like terms: -8 + 8 = 0
0 + x = 12.68857754 + 8
x = 12.68857754 + 8

Combine like terms: 12.68857754 + 8 = 20.68857754
x = 20.68857754

Simplifying
x = 20.68857754


Subproblem 2
x + -8 = -12.68857754

Simplifying
x + -8 = -12.68857754

Reorder the terms:
-8 + x = -12.68857754

Solving
-8 + x = -12.68857754

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = -12.68857754 + 8

Combine like terms: -8 + 8 = 0
0 + x = -12.68857754 + 8
x = -12.68857754 + 8

Combine like terms: -12.68857754 + 8 = -4.68857754
x = -4.68857754

Simplifying
x = -4.68857754


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.68857754, -4.68857754}
Solution
x = {20.68857754, -4.68857754}

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