4a^2+16a+51=-2

Solution for 4a^2+16a+51=-2 equation:

Simplifying
4a2 + 16a + 51 = -2

Reorder the terms:
51 + 16a + 4a2 = -2

Solving
51 + 16a + 4a2 = -2

Solving for variable 'a'.

Reorder the terms:
51 + 2 + 16a + 4a2 = -2 + 2

Combine like terms: 51 + 2 = 53
53 + 16a + 4a2 = -2 + 2

Combine like terms: -2 + 2 = 0
53 + 16a + 4a2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
13.25 + 4a + a2 = 0

Move the constant term to the right:

Add '-13.25' to each side of the equation.
13.25 + 4a + -13.25 + a2 = 0 + -13.25

Reorder the terms:
13.25 + -13.25 + 4a + a2 = 0 + -13.25

Combine like terms: 13.25 + -13.25 = 0.00
0.00 + 4a + a2 = 0 + -13.25
4a + a2 = 0 + -13.25

Combine like terms: 0 + -13.25 = -13.25
4a + a2 = -13.25

The a term is 4a.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4a + 4 + a2 = -13.25 + 4

Reorder the terms:
4 + 4a + a2 = -13.25 + 4

Combine like terms: -13.25 + 4 = -9.25
4 + 4a + a2 = -9.25

Factor a perfect square on the left side:
(a + 2)(a + 2) = -9.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.