x^2+0.83x-0.166=0

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Solution for x^2+0.83x-0.166=0 equation: 


Simplifying
x2 + 0.83x + -0.166 = 0

Reorder the terms:
-0.166 + 0.83x + x2 = 0

Solving
-0.166 + 0.83x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.166' to each side of the equation.
-0.166 + 0.83x + 0.166 + x2 = 0 + 0.166

Reorder the terms:
-0.166 + 0.166 + 0.83x + x2 = 0 + 0.166

Combine like terms: -0.166 + 0.166 = 0.000
0.000 + 0.83x + x2 = 0 + 0.166
0.83x + x2 = 0 + 0.166

Combine like terms: 0 + 0.166 = 0.166
0.83x + x2 = 0.166

The x term is 0.83x.  Take half its coefficient (0.415).
Square it (0.172225) and add it to both sides.

Add '0.172225' to each side of the equation.
0.83x + 0.172225 + x2 = 0.166 + 0.172225

Reorder the terms:
0.172225 + 0.83x + x2 = 0.166 + 0.172225

Combine like terms: 0.166 + 0.172225 = 0.338225
0.172225 + 0.83x + x2 = 0.338225

Factor a perfect square on the left side:
(x + 0.415)(x + 0.415) = 0.338225

Calculate the square root of the right side: 0.581571148

Break this problem into two subproblems by setting 
(x + 0.415) equal to 0.581571148 and -0.581571148.


Subproblem 1
x + 0.415 = 0.581571148

Simplifying
x + 0.415 = 0.581571148

Reorder the terms:
0.415 + x = 0.581571148

Solving
0.415 + x = 0.581571148

Solving for variable 'x'.

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

Add '-0.415' to each side of the equation.
0.415 + -0.415 + x = 0.581571148 + -0.415

Combine like terms: 0.415 + -0.415 = 0.000
0.000 + x = 0.581571148 + -0.415
x = 0.581571148 + -0.415

Combine like terms: 0.581571148 + -0.415 = 0.166571148
x = 0.166571148

Simplifying
x = 0.166571148


Subproblem 2
x + 0.415 = -0.581571148

Simplifying
x + 0.415 = -0.581571148

Reorder the terms:
0.415 + x = -0.581571148

Solving
0.415 + x = -0.581571148

Solving for variable 'x'.

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

Add '-0.415' to each side of the equation.
0.415 + -0.415 + x = -0.581571148 + -0.415

Combine like terms: 0.415 + -0.415 = 0.000
0.000 + x = -0.581571148 + -0.415
x = -0.581571148 + -0.415

Combine like terms: -0.581571148 + -0.415 = -0.996571148
x = -0.996571148

Simplifying
x = -0.996571148


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.166571148, -0.996571148}

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