-x^2+x+1=5

Solution for -x^2+x+1=5 equation:

Simplifying
-1x2 + x + 1 = 5

Reorder the terms:
1 + x + -1x2 = 5

Solving
1 + x + -1x2 = 5

Solving for variable 'x'.

Reorder the terms:
1 + -5 + x + -1x2 = 5 + -5

Combine like terms: 1 + -5 = -4
-4 + x + -1x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-4 + x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
4 + -1x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -1x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -1x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x + x2 = 0 + -4
-1x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-1x + x2 = -4

The x term is x.  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 = -4 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -4 + 0.25

Combine like terms: -4 + 0.25 = -3.75
0.25 + -1x + x2 = -3.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -3.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.