z^2-10z+61=0

Solution for z^2-10z+61=0 equation:

Simplifying
z2 + -10z + 61 = 0

Reorder the terms:
61 + -10z + z2 = 0

Solving
61 + -10z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-61' to each side of the equation.
61 + -10z + -61 + z2 = 0 + -61

Reorder the terms:
61 + -61 + -10z + z2 = 0 + -61

Combine like terms: 61 + -61 = 0
0 + -10z + z2 = 0 + -61
-10z + z2 = 0 + -61

Combine like terms: 0 + -61 = -61
-10z + z2 = -61

The z term is -10z.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10z + 25 + z2 = -61 + 25

Reorder the terms:
25 + -10z + z2 = -61 + 25

Combine like terms: -61 + 25 = -36
25 + -10z + z2 = -36

Factor a perfect square on the left side:
(z + -5)(z + -5) = -36

Can't calculate square root of the right side.

The solution to this equation could not be determined.