10z^2-5z=-1

Solution for 10z^2-5z=-1 equation:

Simplifying
10z2 + -5z = -1

Reorder the terms:
-5z + 10z2 = -1

Solving
-5z + 10z2 = -1

Solving for variable 'z'.

Reorder the terms:
1 + -5z + 10z2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + -5z + 10z2 = 0

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

Divide each side by '10'.
0.1 + -0.5z + z2 = 0

Move the constant term to the right:

Add '-0.1' to each side of the equation.
0.1 + -0.5z + -0.1 + z2 = 0 + -0.1

Reorder the terms:
0.1 + -0.1 + -0.5z + z2 = 0 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + -0.5z + z2 = 0 + -0.1
-0.5z + z2 = 0 + -0.1

Combine like terms: 0 + -0.1 = -0.1
-0.5z + z2 = -0.1

The z term is -0.5z.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5z + 0.0625 + z2 = -0.1 + 0.0625

Reorder the terms:
0.0625 + -0.5z + z2 = -0.1 + 0.0625

Combine like terms: -0.1 + 0.0625 = -0.0375
0.0625 + -0.5z + z2 = -0.0375

Factor a perfect square on the left side:
(z + -0.25)(z + -0.25) = -0.0375

Can't calculate square root of the right side.

The solution to this equation could not be determined.