5y^2-y=-1

Solution for 5y^2-y=-1 equation:

Simplifying
5y2 + -1y = -1

Reorder the terms:
-1y + 5y2 = -1

Solving
-1y + 5y2 = -1

Solving for variable 'y'.

Reorder the terms:
1 + -1y + 5y2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + -1y + 5y2 = 0

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

Divide each side by '5'.
0.2 + -0.2y + y2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -0.2y + -0.2 + y2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -0.2y + y2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -0.2y + y2 = 0 + -0.2
-0.2y + y2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-0.2y + y2 = -0.2

The y term is -0.2y.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2y + 0.01 + y2 = -0.2 + 0.01

Reorder the terms:
0.01 + -0.2y + y2 = -0.2 + 0.01

Combine like terms: -0.2 + 0.01 = -0.19
0.01 + -0.2y + y2 = -0.19

Factor a perfect square on the left side:
(y + -0.1)(y + -0.1) = -0.19

Can't calculate square root of the right side.

The solution to this equation could not be determined.