2x^2-16x+14=6

Solution for 2x^2-16x+14=6 equation:

Simplifying
2x2 + -16x + 14 = 6

Reorder the terms:
14 + -16x + 2x2 = 6

Solving
14 + -16x + 2x2 = 6

Solving for variable 'x'.

Reorder the terms:
14 + -6 + -16x + 2x2 = 6 + -6

Combine like terms: 14 + -6 = 8
8 + -16x + 2x2 = 6 + -6

Combine like terms: 6 + -6 = 0
8 + -16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -8x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
4 + -8x + x2 = 0

Solving
4 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -8x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -8x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -8x + x2 = 0 + -4
-8x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-8x + x2 = -4

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 = -4 + 16

Reorder the terms:
16 + -8x + x2 = -4 + 16

Combine like terms: -4 + 16 = 12
16 + -8x + x2 = 12

Factor a perfect square on the left side:
(x + -4)(x + -4) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x + -4) equal to 3.464101615 and -3.464101615.

Subproblem 1
x + -4 = 3.464101615

Simplifying
x + -4 = 3.464101615

Reorder the terms:
-4 + x = 3.464101615

Solving
-4 + x = 3.464101615

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + x = 3.464101615 + 4

Combine like terms: -4 + 4 = 0
0 + x = 3.464101615 + 4
x = 3.464101615 + 4

Combine like terms: 3.464101615 + 4 = 7.464101615
x = 7.464101615

Simplifying
x = 7.464101615

Subproblem 2
x + -4 = -3.464101615

Simplifying
x + -4 = -3.464101615

Reorder the terms:
-4 + x = -3.464101615

Solving
-4 + x = -3.464101615

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + x = -3.464101615 + 4

Combine like terms: -4 + 4 = 0
0 + x = -3.464101615 + 4
x = -3.464101615 + 4

Combine like terms: -3.464101615 + 4 = 0.535898385
x = 0.535898385

Simplifying
x = 0.535898385

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.464101615, 0.535898385}
Solution
x = {7.464101615, 0.535898385}