X^2-X-0.6=0

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Solution for X^2-X-0.6=0 equation: 


Simplifying
X2 + -1X + -0.6 = 0

Reorder the terms:
-0.6 + -1X + X2 = 0

Solving
-0.6 + -1X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -1X + 0.6 + X2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -1X + X2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -1X + X2 = 0 + 0.6
-1X + X2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-1X + X2 = 0.6

The X term is -1X.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1X + 0.25 + X2 = 0.6 + 0.25

Reorder the terms:
0.25 + -1X + X2 = 0.6 + 0.25

Combine like terms: 0.6 + 0.25 = 0.85
0.25 + -1X + X2 = 0.85

Factor a perfect square on the left side:
(X + -0.5)(X + -0.5) = 0.85

Calculate the square root of the right side: 0.921954446

Break this problem into two subproblems by setting 
(X + -0.5) equal to 0.921954446 and -0.921954446.


Subproblem 1
X + -0.5 = 0.921954446

Simplifying
X + -0.5 = 0.921954446

Reorder the terms:
-0.5 + X = 0.921954446

Solving
-0.5 + X = 0.921954446

Solving for variable 'X'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + X = 0.921954446 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + X = 0.921954446 + 0.5
X = 0.921954446 + 0.5

Combine like terms: 0.921954446 + 0.5 = 1.421954446
X = 1.421954446

Simplifying
X = 1.421954446


Subproblem 2
X + -0.5 = -0.921954446

Simplifying
X + -0.5 = -0.921954446

Reorder the terms:
-0.5 + X = -0.921954446

Solving
-0.5 + X = -0.921954446

Solving for variable 'X'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + X = -0.921954446 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + X = -0.921954446 + 0.5
X = -0.921954446 + 0.5

Combine like terms: -0.921954446 + 0.5 = -0.421954446
X = -0.421954446

Simplifying
X = -0.421954446


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {1.421954446, -0.421954446}

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