6x^2+49=-6x-14

Solution for 6x^2+49=-6x-14 equation:

Simplifying
6x2 + 49 = -6x + -14

Reorder the terms:
49 + 6x2 = -6x + -14

Reorder the terms:
49 + 6x2 = -14 + -6x

Solving
49 + 6x2 = -14 + -6x

Solving for variable 'x'.

Reorder the terms:
49 + 14 + 6x + 6x2 = -14 + -6x + 14 + 6x

Combine like terms: 49 + 14 = 63
63 + 6x + 6x2 = -14 + -6x + 14 + 6x

Reorder the terms:
63 + 6x + 6x2 = -14 + 14 + -6x + 6x

Combine like terms: -14 + 14 = 0
63 + 6x + 6x2 = 0 + -6x + 6x
63 + 6x + 6x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
63 + 6x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(21 + 2x + 2x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(21 + 2x + 2x2)' equal to zero and attempt to solve:

Simplifying
21 + 2x + 2x2 = 0

Solving
21 + 2x + 2x2 = 0

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

Divide each side by '2'.
10.5 + x + x2 = 0

Move the constant term to the right:

Add '-10.5' to each side of the equation.
10.5 + x + -10.5 + x2 = 0 + -10.5

Reorder the terms:
10.5 + -10.5 + x + x2 = 0 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x + x2 = 0 + -10.5
x + x2 = 0 + -10.5

Combine like terms: 0 + -10.5 = -10.5
x + x2 = -10.5

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 = -10.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = -10.5 + 0.25

Combine like terms: -10.5 + 0.25 = -10.25
1.25 + x2 = -10.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -10.25

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.