x^2+0.85x-2.9155=0

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Solution for x^2+0.85x-2.9155=0 equation: 


Simplifying
x2 + 0.85x + -2.9155 = 0

Reorder the terms:
-2.9155 + 0.85x + x2 = 0

Solving
-2.9155 + 0.85x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2.9155' to each side of the equation.
-2.9155 + 0.85x + 2.9155 + x2 = 0 + 2.9155

Reorder the terms:
-2.9155 + 2.9155 + 0.85x + x2 = 0 + 2.9155

Combine like terms: -2.9155 + 2.9155 = 0.0000
0.0000 + 0.85x + x2 = 0 + 2.9155
0.85x + x2 = 0 + 2.9155

Combine like terms: 0 + 2.9155 = 2.9155
0.85x + x2 = 2.9155

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 = 2.9155 + 0.180625

Reorder the terms:
0.180625 + 0.85x + x2 = 2.9155 + 0.180625

Combine like terms: 2.9155 + 0.180625 = 3.096125
0.180625 + 0.85x + x2 = 3.096125

Factor a perfect square on the left side:
(x + 0.425)(x + 0.425) = 3.096125

Calculate the square root of the right side: 1.759580916

Break this problem into two subproblems by setting 
(x + 0.425) equal to 1.759580916 and -1.759580916.


Subproblem 1
x + 0.425 = 1.759580916

Simplifying
x + 0.425 = 1.759580916

Reorder the terms:
0.425 + x = 1.759580916

Solving
0.425 + x = 1.759580916

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 = 1.759580916 + -0.425

Combine like terms: 0.425 + -0.425 = 0.000
0.000 + x = 1.759580916 + -0.425
x = 1.759580916 + -0.425

Combine like terms: 1.759580916 + -0.425 = 1.334580916
x = 1.334580916

Simplifying
x = 1.334580916


Subproblem 2
x + 0.425 = -1.759580916

Simplifying
x + 0.425 = -1.759580916

Reorder the terms:
0.425 + x = -1.759580916

Solving
0.425 + x = -1.759580916

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 = -1.759580916 + -0.425

Combine like terms: 0.425 + -0.425 = 0.000
0.000 + x = -1.759580916 + -0.425
x = -1.759580916 + -0.425

Combine like terms: -1.759580916 + -0.425 = -2.184580916
x = -2.184580916

Simplifying
x = -2.184580916


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.334580916, -2.184580916}

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