a^2+a=-1

Solution for a^2+a=-1 equation:

Simplifying
a2 + a = -1

Reorder the terms:
a + a2 = -1

Solving
a + a2 = -1

Solving for variable 'a'.

Reorder the terms:
1 + a + a2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + a + -1 + a2 = 0 + -1

Reorder the terms:
1 + -1 + a + a2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + a + a2 = 0 + -1
a + a2 = 0 + -1

Combine like terms: 0 + -1 = -1
a + a2 = -1

The a term is a.  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.
a + 0.25 + a2 = -1 + 0.25

Reorder the terms:
0.25 + a + a2 = -1 + 0.25

Combine like terms: -1 + 0.25 = -0.75
0.25 + a + a2 = -0.75

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

Can't calculate square root of the right side.

The solution to this equation could not be determined.