n^2+14n+52=0

Solution for n^2+14n+52=0 equation:

Simplifying
n2 + 14n + 52 = 0

Reorder the terms:
52 + 14n + n2 = 0

Solving
52 + 14n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '-52' to each side of the equation.
52 + 14n + -52 + n2 = 0 + -52

Reorder the terms:
52 + -52 + 14n + n2 = 0 + -52

Combine like terms: 52 + -52 = 0
0 + 14n + n2 = 0 + -52
14n + n2 = 0 + -52

Combine like terms: 0 + -52 = -52
14n + n2 = -52

The n term is 14n.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14n + 49 + n2 = -52 + 49

Reorder the terms:
49 + 14n + n2 = -52 + 49

Combine like terms: -52 + 49 = -3
49 + 14n + n2 = -3

Factor a perfect square on the left side:
(n + 7)(n + 7) = -3

Can't calculate square root of the right side.

The solution to this equation could not be determined.