5x^2+4x=-1

Solution for 5x^2+4x=-1 equation:

Simplifying
5x2 + 4x = -1

Reorder the terms:
4x + 5x2 = -1

Solving
4x + 5x2 = -1

Solving for variable 'x'.

Reorder the terms:
1 + 4x + 5x2 = -1 + 1

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

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

Divide each side by '5'.
0.2 + 0.8x + x2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 0.8x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + 0.8x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 0.8x + x2 = 0 + -0.2
0.8x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
0.8x + x2 = -0.2

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = -0.2 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = -0.2 + 0.16

Combine like terms: -0.2 + 0.16 = -0.04
0.16 + 0.8x + x2 = -0.04

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = -0.04

Can't calculate square root of the right side.

The solution to this equation could not be determined.