X^2+0.167X-0.167=0

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Solution for X^2+0.167X-0.167=0 equation: 


Simplifying
X2 + 0.167X + -0.167 = 0

Reorder the terms:
-0.167 + 0.167X + X2 = 0

Solving
-0.167 + 0.167X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '0.167' to each side of the equation.
-0.167 + 0.167X + 0.167 + X2 = 0 + 0.167

Reorder the terms:
-0.167 + 0.167 + 0.167X + X2 = 0 + 0.167

Combine like terms: -0.167 + 0.167 = 0.000
0.000 + 0.167X + X2 = 0 + 0.167
0.167X + X2 = 0 + 0.167

Combine like terms: 0 + 0.167 = 0.167
0.167X + X2 = 0.167

The X term is 0.167X.  Take half its coefficient (0.0835).
Square it (0.00697225) and add it to both sides.

Add '0.00697225' to each side of the equation.
0.167X + 0.00697225 + X2 = 0.167 + 0.00697225

Reorder the terms:
0.00697225 + 0.167X + X2 = 0.167 + 0.00697225

Combine like terms: 0.167 + 0.00697225 = 0.17397225
0.00697225 + 0.167X + X2 = 0.17397225

Factor a perfect square on the left side:
(X + 0.0835)(X + 0.0835) = 0.17397225

Calculate the square root of the right side: 0.417099808

Break this problem into two subproblems by setting 
(X + 0.0835) equal to 0.417099808 and -0.417099808.


Subproblem 1
X + 0.0835 = 0.417099808

Simplifying
X + 0.0835 = 0.417099808

Reorder the terms:
0.0835 + X = 0.417099808

Solving
0.0835 + X = 0.417099808

Solving for variable 'X'.

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

Add '-0.0835' to each side of the equation.
0.0835 + -0.0835 + X = 0.417099808 + -0.0835

Combine like terms: 0.0835 + -0.0835 = 0.0000
0.0000 + X = 0.417099808 + -0.0835
X = 0.417099808 + -0.0835

Combine like terms: 0.417099808 + -0.0835 = 0.333599808
X = 0.333599808

Simplifying
X = 0.333599808


Subproblem 2
X + 0.0835 = -0.417099808

Simplifying
X + 0.0835 = -0.417099808

Reorder the terms:
0.0835 + X = -0.417099808

Solving
0.0835 + X = -0.417099808

Solving for variable 'X'.

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

Add '-0.0835' to each side of the equation.
0.0835 + -0.0835 + X = -0.417099808 + -0.0835

Combine like terms: 0.0835 + -0.0835 = 0.0000
0.0000 + X = -0.417099808 + -0.0835
X = -0.417099808 + -0.0835

Combine like terms: -0.417099808 + -0.0835 = -0.500599808
X = -0.500599808

Simplifying
X = -0.500599808


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.333599808, -0.500599808}

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