4(x^2-8x+16)+14=0

Solution for 4(x^2-8x+16)+14=0 equation:

Simplifying
4(x2 + -8x + 16) + 14 = 0

Reorder the terms:
4(16 + -8x + x2) + 14 = 0
(16 * 4 + -8x * 4 + x2 * 4) + 14 = 0
(64 + -32x + 4x2) + 14 = 0

Reorder the terms:
64 + 14 + -32x + 4x2 = 0

Combine like terms: 64 + 14 = 78
78 + -32x + 4x2 = 0

Solving
78 + -32x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(39 + -16x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(39 + -16x + 2x2)' equal to zero and attempt to solve:

Simplifying
39 + -16x + 2x2 = 0

Solving
39 + -16x + 2x2 = 0

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

Divide each side by '2'.
19.5 + -8x + x2 = 0

Move the constant term to the right:

Add '-19.5' to each side of the equation.
19.5 + -8x + -19.5 + x2 = 0 + -19.5

Reorder the terms:
19.5 + -19.5 + -8x + x2 = 0 + -19.5

Combine like terms: 19.5 + -19.5 = 0.0
0.0 + -8x + x2 = 0 + -19.5
-8x + x2 = 0 + -19.5

Combine like terms: 0 + -19.5 = -19.5
-8x + x2 = -19.5

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 = -19.5 + 16

Reorder the terms:
16 + -8x + x2 = -19.5 + 16

Combine like terms: -19.5 + 16 = -3.5
16 + -8x + x2 = -3.5

Factor a perfect square on the left side:
(x + -4)(x + -4) = -3.5

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.