x^2-16x-85=0

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Solution for x^2-16x-85=0 equation: 


Simplifying
x2 + -16x + -85 = 0

Reorder the terms:
-85 + -16x + x2 = 0

Solving
-85 + -16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '85' to each side of the equation.
-85 + -16x + 85 + x2 = 0 + 85

Reorder the terms:
-85 + 85 + -16x + x2 = 0 + 85

Combine like terms: -85 + 85 = 0
0 + -16x + x2 = 0 + 85
-16x + x2 = 0 + 85

Combine like terms: 0 + 85 = 85
-16x + x2 = 85

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 = 85 + 64

Reorder the terms:
64 + -16x + x2 = 85 + 64

Combine like terms: 85 + 64 = 149
64 + -16x + x2 = 149

Factor a perfect square on the left side:
(x + -8)(x + -8) = 149

Calculate the square root of the right side: 12.206555616

Break this problem into two subproblems by setting 
(x + -8) equal to 12.206555616 and -12.206555616.


Subproblem 1
x + -8 = 12.206555616

Simplifying
x + -8 = 12.206555616

Reorder the terms:
-8 + x = 12.206555616

Solving
-8 + x = 12.206555616

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 = 12.206555616 + 8

Combine like terms: -8 + 8 = 0
0 + x = 12.206555616 + 8
x = 12.206555616 + 8

Combine like terms: 12.206555616 + 8 = 20.206555616
x = 20.206555616

Simplifying
x = 20.206555616


Subproblem 2
x + -8 = -12.206555616

Simplifying
x + -8 = -12.206555616

Reorder the terms:
-8 + x = -12.206555616

Solving
-8 + x = -12.206555616

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 = -12.206555616 + 8

Combine like terms: -8 + 8 = 0
0 + x = -12.206555616 + 8
x = -12.206555616 + 8

Combine like terms: -12.206555616 + 8 = -4.206555616
x = -4.206555616

Simplifying
x = -4.206555616


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.206555616, -4.206555616}

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