a^2+10a+33=0

Solution for a^2+10a+33=0 equation:

Simplifying
a2 + 10a + 33 = 0

Reorder the terms:
33 + 10a + a2 = 0

Solving
33 + 10a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-33' to each side of the equation.
33 + 10a + -33 + a2 = 0 + -33

Reorder the terms:
33 + -33 + 10a + a2 = 0 + -33

Combine like terms: 33 + -33 = 0
0 + 10a + a2 = 0 + -33
10a + a2 = 0 + -33

Combine like terms: 0 + -33 = -33
10a + a2 = -33

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

Add '25' to each side of the equation.
10a + 25 + a2 = -33 + 25

Reorder the terms:
25 + 10a + a2 = -33 + 25

Combine like terms: -33 + 25 = -8
25 + 10a + a2 = -8

Factor a perfect square on the left side:
(a + 5)(a + 5) = -8

Can't calculate square root of the right side.

The solution to this equation could not be determined.