x^2-10x-85=0

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Solution for x^2-10x-85=0 equation: 


Simplifying
x2 + -10x + -85 = 0

Reorder the terms:
-85 + -10x + x2 = 0

Solving
-85 + -10x + 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 + -10x + 85 + x2 = 0 + 85

Reorder the terms:
-85 + 85 + -10x + x2 = 0 + 85

Combine like terms: -85 + 85 = 0
0 + -10x + x2 = 0 + 85
-10x + x2 = 0 + 85

Combine like terms: 0 + 85 = 85
-10x + x2 = 85

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 85 + 25

Reorder the terms:
25 + -10x + x2 = 85 + 25

Combine like terms: 85 + 25 = 110
25 + -10x + x2 = 110

Factor a perfect square on the left side:
(x + -5)(x + -5) = 110

Calculate the square root of the right side: 10.488088482

Break this problem into two subproblems by setting 
(x + -5) equal to 10.488088482 and -10.488088482.


Subproblem 1
x + -5 = 10.488088482

Simplifying
x + -5 = 10.488088482

Reorder the terms:
-5 + x = 10.488088482

Solving
-5 + x = 10.488088482

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 10.488088482 + 5

Combine like terms: -5 + 5 = 0
0 + x = 10.488088482 + 5
x = 10.488088482 + 5

Combine like terms: 10.488088482 + 5 = 15.488088482
x = 15.488088482

Simplifying
x = 15.488088482


Subproblem 2
x + -5 = -10.488088482

Simplifying
x + -5 = -10.488088482

Reorder the terms:
-5 + x = -10.488088482

Solving
-5 + x = -10.488088482

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -10.488088482 + 5

Combine like terms: -5 + 5 = 0
0 + x = -10.488088482 + 5
x = -10.488088482 + 5

Combine like terms: -10.488088482 + 5 = -5.488088482
x = -5.488088482

Simplifying
x = -5.488088482


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.488088482, -5.488088482}

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