x^2=x-1

Solution for x^2=x-1 equation:

Simplifying
x2 = x + -1

Reorder the terms:
x2 = -1 + x

Solving
x2 = -1 + x

Solving for variable 'x'.

Reorder the terms:
1 + -1x + x2 = -1 + x + 1 + -1x

Reorder the terms:
1 + -1x + x2 = -1 + 1 + x + -1x

Combine like terms: -1 + 1 = 0
1 + -1x + x2 = 0 + x + -1x
1 + -1x + x2 = x + -1x

Combine like terms: x + -1x = 0
1 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -1x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -1x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x + x2 = 0 + -1
-1x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-1x + x2 = -1

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 = -1 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -1 + 0.25

Combine like terms: -1 + 0.25 = -0.75
0.25 + -1x + x2 = -0.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -0.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.