4x^2+4x+21=0

Solution for 4x^2+4x+21=0 equation:

Simplifying
4x2 + 4x + 21 = 0

Reorder the terms:
21 + 4x + 4x2 = 0

Solving
21 + 4x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
5.25 + x + x2 = 0

Move the constant term to the right:

Add '-5.25' to each side of the equation.
5.25 + x + -5.25 + x2 = 0 + -5.25

Reorder the terms:
5.25 + -5.25 + x + x2 = 0 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
0.00 + x + x2 = 0 + -5.25
x + x2 = 0 + -5.25

Combine like terms: 0 + -5.25 = -5.25
x + x2 = -5.25

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = -5.25 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = -5.25 + 0.25

Combine like terms: -5.25 + 0.25 = -5
1.25 + x2 = -5

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -5

Can't calculate square root of the right side.

The solution to this equation could not be determined.