x^2+0.85x-10.331=0

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Solution for x^2+0.85x-10.331=0 equation: 


Simplifying
x2 + 0.85x + -10.331 = 0

Reorder the terms:
-10.331 + 0.85x + x2 = 0

Solving
-10.331 + 0.85x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '10.331' to each side of the equation.
-10.331 + 0.85x + 10.331 + x2 = 0 + 10.331

Reorder the terms:
-10.331 + 10.331 + 0.85x + x2 = 0 + 10.331

Combine like terms: -10.331 + 10.331 = 0.000
0.000 + 0.85x + x2 = 0 + 10.331
0.85x + x2 = 0 + 10.331

Combine like terms: 0 + 10.331 = 10.331
0.85x + x2 = 10.331

The x term is 0.85x.  Take half its coefficient (0.425).
Square it (0.180625) and add it to both sides.

Add '0.180625' to each side of the equation.
0.85x + 0.180625 + x2 = 10.331 + 0.180625

Reorder the terms:
0.180625 + 0.85x + x2 = 10.331 + 0.180625

Combine like terms: 10.331 + 0.180625 = 10.511625
0.180625 + 0.85x + x2 = 10.511625

Factor a perfect square on the left side:
(x + 0.425)(x + 0.425) = 10.511625

Calculate the square root of the right side: 3.242163629

Break this problem into two subproblems by setting 
(x + 0.425) equal to 3.242163629 and -3.242163629.


Subproblem 1
x + 0.425 = 3.242163629

Simplifying
x + 0.425 = 3.242163629

Reorder the terms:
0.425 + x = 3.242163629

Solving
0.425 + x = 3.242163629

Solving for variable 'x'.

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

Add '-0.425' to each side of the equation.
0.425 + -0.425 + x = 3.242163629 + -0.425

Combine like terms: 0.425 + -0.425 = 0.000
0.000 + x = 3.242163629 + -0.425
x = 3.242163629 + -0.425

Combine like terms: 3.242163629 + -0.425 = 2.817163629
x = 2.817163629

Simplifying
x = 2.817163629


Subproblem 2
x + 0.425 = -3.242163629

Simplifying
x + 0.425 = -3.242163629

Reorder the terms:
0.425 + x = -3.242163629

Solving
0.425 + x = -3.242163629

Solving for variable 'x'.

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

Add '-0.425' to each side of the equation.
0.425 + -0.425 + x = -3.242163629 + -0.425

Combine like terms: 0.425 + -0.425 = 0.000
0.000 + x = -3.242163629 + -0.425
x = -3.242163629 + -0.425

Combine like terms: -3.242163629 + -0.425 = -3.667163629
x = -3.667163629

Simplifying
x = -3.667163629


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.817163629, -3.667163629}

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