1=-x^2+x-3

Solution for 1=-x^2+x-3 equation:

Simplifying
1 = -1x2 + x + -3

Reorder the terms:
1 = -3 + x + -1x2

Solving
1 = -3 + x + -1x2

Solving for variable 'x'.

Combine like terms: 1 + 3 = 4
4 + -1x + x2 = -3 + x + -1x2 + 3 + -1x + x2

Reorder the terms:
4 + -1x + x2 = -3 + 3 + x + -1x + -1x2 + x2

Combine like terms: -3 + 3 = 0
4 + -1x + x2 = 0 + x + -1x + -1x2 + x2
4 + -1x + x2 = x + -1x + -1x2 + x2

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

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

Begin completing the square.

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 -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 = -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.