a^2+3a+52=0

Solution for a^2+3a+52=0 equation:

Simplifying
a2 + 3a + 52 = 0

Reorder the terms:
52 + 3a + a2 = 0

Solving
52 + 3a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-52' to each side of the equation.
52 + 3a + -52 + a2 = 0 + -52

Reorder the terms:
52 + -52 + 3a + a2 = 0 + -52

Combine like terms: 52 + -52 = 0
0 + 3a + a2 = 0 + -52
3a + a2 = 0 + -52

Combine like terms: 0 + -52 = -52
3a + a2 = -52

The a term is 3a.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3a + 2.25 + a2 = -52 + 2.25

Reorder the terms:
2.25 + 3a + a2 = -52 + 2.25

Combine like terms: -52 + 2.25 = -49.75
2.25 + 3a + a2 = -49.75

Factor a perfect square on the left side:
(a + 1.5)(a + 1.5) = -49.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.