2(x^2+8x+21)=0

Solution for 2(x^2+8x+21)=0 equation:

Simplifying
2(x2 + 8x + 21) = 0

Reorder the terms:
2(21 + 8x + x2) = 0
(21 * 2 + 8x * 2 + x2 * 2) = 0
(42 + 16x + 2x2) = 0

Solving
42 + 16x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + 8x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(21 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
21 + 8x + x2 = 0

Solving
21 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + 8x + -21 + x2 = 0 + -21

Reorder the terms:
21 + -21 + 8x + x2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + 8x + x2 = 0 + -21
8x + x2 = 0 + -21

Combine like terms: 0 + -21 = -21
8x + x2 = -21

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -21 + 16

Reorder the terms:
16 + 8x + x2 = -21 + 16

Combine like terms: -21 + 16 = -5
16 + 8x + x2 = -5

Factor a perfect square on the left side:
(x + 4)(x + 4) = -5

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.