x^2+0.85x-8.058=0

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Solution for x^2+0.85x-8.058=0 equation: 


Simplifying
x2 + 0.85x + -8.058 = 0

Reorder the terms:
-8.058 + 0.85x + x2 = 0

Solving
-8.058 + 0.85x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '8.058' to each side of the equation.
-8.058 + 0.85x + 8.058 + x2 = 0 + 8.058

Reorder the terms:
-8.058 + 8.058 + 0.85x + x2 = 0 + 8.058

Combine like terms: -8.058 + 8.058 = 0.000
0.000 + 0.85x + x2 = 0 + 8.058
0.85x + x2 = 0 + 8.058

Combine like terms: 0 + 8.058 = 8.058
0.85x + x2 = 8.058

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 = 8.058 + 0.180625

Reorder the terms:
0.180625 + 0.85x + x2 = 8.058 + 0.180625

Combine like terms: 8.058 + 0.180625 = 8.238625
0.180625 + 0.85x + x2 = 8.238625

Factor a perfect square on the left side:
(x + 0.425)(x + 0.425) = 8.238625

Calculate the square root of the right side: 2.870300507

Break this problem into two subproblems by setting 
(x + 0.425) equal to 2.870300507 and -2.870300507.


Subproblem 1
x + 0.425 = 2.870300507

Simplifying
x + 0.425 = 2.870300507

Reorder the terms:
0.425 + x = 2.870300507

Solving
0.425 + x = 2.870300507

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 = 2.870300507 + -0.425

Combine like terms: 0.425 + -0.425 = 0.000
0.000 + x = 2.870300507 + -0.425
x = 2.870300507 + -0.425

Combine like terms: 2.870300507 + -0.425 = 2.445300507
x = 2.445300507

Simplifying
x = 2.445300507


Subproblem 2
x + 0.425 = -2.870300507

Simplifying
x + 0.425 = -2.870300507

Reorder the terms:
0.425 + x = -2.870300507

Solving
0.425 + x = -2.870300507

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 = -2.870300507 + -0.425

Combine like terms: 0.425 + -0.425 = 0.000
0.000 + x = -2.870300507 + -0.425
x = -2.870300507 + -0.425

Combine like terms: -2.870300507 + -0.425 = -3.295300507
x = -3.295300507

Simplifying
x = -3.295300507


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.445300507, -3.295300507}

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