x^2-13x+61=0

Solution for x^2-13x+61=0 equation:

Simplifying
x2 + -13x + 61 = 0

Reorder the terms:
61 + -13x + x2 = 0

Solving
61 + -13x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-61' to each side of the equation.
61 + -13x + -61 + x2 = 0 + -61

Reorder the terms:
61 + -61 + -13x + x2 = 0 + -61

Combine like terms: 61 + -61 = 0
0 + -13x + x2 = 0 + -61
-13x + x2 = 0 + -61

Combine like terms: 0 + -61 = -61
-13x + x2 = -61

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = -61 + 42.25

Reorder the terms:
42.25 + -13x + x2 = -61 + 42.25

Combine like terms: -61 + 42.25 = -18.75
42.25 + -13x + x2 = -18.75

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = -18.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.