x^2-22x-85=0

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Solution for x^2-22x-85=0 equation: 


Simplifying
x2 + -22x + -85 = 0

Reorder the terms:
-85 + -22x + x2 = 0

Solving
-85 + -22x + 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 + -22x + 85 + x2 = 0 + 85

Reorder the terms:
-85 + 85 + -22x + x2 = 0 + 85

Combine like terms: -85 + 85 = 0
0 + -22x + x2 = 0 + 85
-22x + x2 = 0 + 85

Combine like terms: 0 + 85 = 85
-22x + x2 = 85

The x term is -22x.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22x + 121 + x2 = 85 + 121

Reorder the terms:
121 + -22x + x2 = 85 + 121

Combine like terms: 85 + 121 = 206
121 + -22x + x2 = 206

Factor a perfect square on the left side:
(x + -11)(x + -11) = 206

Calculate the square root of the right side: 14.352700094

Break this problem into two subproblems by setting 
(x + -11) equal to 14.352700094 and -14.352700094.


Subproblem 1
x + -11 = 14.352700094

Simplifying
x + -11 = 14.352700094

Reorder the terms:
-11 + x = 14.352700094

Solving
-11 + x = 14.352700094

Solving for variable 'x'.

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

Add '11' to each side of the equation.
-11 + 11 + x = 14.352700094 + 11

Combine like terms: -11 + 11 = 0
0 + x = 14.352700094 + 11
x = 14.352700094 + 11

Combine like terms: 14.352700094 + 11 = 25.352700094
x = 25.352700094

Simplifying
x = 25.352700094


Subproblem 2
x + -11 = -14.352700094

Simplifying
x + -11 = -14.352700094

Reorder the terms:
-11 + x = -14.352700094

Solving
-11 + x = -14.352700094

Solving for variable 'x'.

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

Add '11' to each side of the equation.
-11 + 11 + x = -14.352700094 + 11

Combine like terms: -11 + 11 = 0
0 + x = -14.352700094 + 11
x = -14.352700094 + 11

Combine like terms: -14.352700094 + 11 = -3.352700094
x = -3.352700094

Simplifying
x = -3.352700094


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {25.352700094, -3.352700094}

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