y^2+13y+52=0

Solution for y^2+13y+52=0 equation:

Simplifying
y2 + 13y + 52 = 0

Reorder the terms:
52 + 13y + y2 = 0

Solving
52 + 13y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-52' to each side of the equation.
52 + 13y + -52 + y2 = 0 + -52

Reorder the terms:
52 + -52 + 13y + y2 = 0 + -52

Combine like terms: 52 + -52 = 0
0 + 13y + y2 = 0 + -52
13y + y2 = 0 + -52

Combine like terms: 0 + -52 = -52
13y + y2 = -52

The y term is 13y.  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.
13y + 42.25 + y2 = -52 + 42.25

Reorder the terms:
42.25 + 13y + y2 = -52 + 42.25

Combine like terms: -52 + 42.25 = -9.75
42.25 + 13y + y2 = -9.75

Factor a perfect square on the left side:
(y + 6.5)(y + 6.5) = -9.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.