x^2-0.5x-0.5=0

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Solution for x^2-0.5x-0.5=0 equation: 


Simplifying
x2 + -0.5x + -0.5 = 0

Reorder the terms:
-0.5 + -0.5x + x2 = 0

Solving
-0.5 + -0.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -0.5x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -0.5x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -0.5x + x2 = 0 + 0.5
-0.5x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-0.5x + x2 = 0.5

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 0.5 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 0.5 + 0.0625

Combine like terms: 0.5 + 0.0625 = 0.5625
0.0625 + -0.5x + x2 = 0.5625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 0.5625

Calculate the square root of the right side: 0.75

Break this problem into two subproblems by setting 
(x + -0.25) equal to 0.75 and -0.75.


Subproblem 1
x + -0.25 = 0.75

Simplifying
x + -0.25 = 0.75

Reorder the terms:
-0.25 + x = 0.75

Solving
-0.25 + x = 0.75

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 0.75 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 0.75 + 0.25
x = 0.75 + 0.25

Combine like terms: 0.75 + 0.25 = 1
x = 1

Simplifying
x = 1


Subproblem 2
x + -0.25 = -0.75

Simplifying
x + -0.25 = -0.75

Reorder the terms:
-0.25 + x = -0.75

Solving
-0.25 + x = -0.75

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -0.75 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -0.75 + 0.25
x = -0.75 + 0.25

Combine like terms: -0.75 + 0.25 = -0.5
x = -0.5

Simplifying
x = -0.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1, -0.5}

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