16x^2-8x-3=5x^2-2x+1

Solution for 16x^2-8x-3=5x^2-2x+1 equation:

Simplifying
16x2 + -8x + -3 = 5x2 + -2x + 1

Reorder the terms:
-3 + -8x + 16x2 = 5x2 + -2x + 1

Reorder the terms:
-3 + -8x + 16x2 = 1 + -2x + 5x2

Solving
-3 + -8x + 16x2 = 1 + -2x + 5x2

Solving for variable 'x'.

Reorder the terms:
-3 + -1 + -8x + 2x + 16x2 + -5x2 = 1 + -2x + 5x2 + -1 + 2x + -5x2

Combine like terms: -3 + -1 = -4
-4 + -8x + 2x + 16x2 + -5x2 = 1 + -2x + 5x2 + -1 + 2x + -5x2

Combine like terms: -8x + 2x = -6x
-4 + -6x + 16x2 + -5x2 = 1 + -2x + 5x2 + -1 + 2x + -5x2

Combine like terms: 16x2 + -5x2 = 11x2
-4 + -6x + 11x2 = 1 + -2x + 5x2 + -1 + 2x + -5x2

Reorder the terms:
-4 + -6x + 11x2 = 1 + -1 + -2x + 2x + 5x2 + -5x2

Combine like terms: 1 + -1 = 0
-4 + -6x + 11x2 = 0 + -2x + 2x + 5x2 + -5x2
-4 + -6x + 11x2 = -2x + 2x + 5x2 + -5x2

Combine like terms: -2x + 2x = 0
-4 + -6x + 11x2 = 0 + 5x2 + -5x2
-4 + -6x + 11x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-4 + -6x + 11x2 = 0

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

Divide each side by '11'.
-0.3636363636 + -0.5454545455x + x2 = 0

Move the constant term to the right:

Add '0.3636363636' to each side of the equation.
-0.3636363636 + -0.5454545455x + 0.3636363636 + x2 = 0 + 0.3636363636

Reorder the terms:
-0.3636363636 + 0.3636363636 + -0.5454545455x + x2 = 0 + 0.3636363636

Combine like terms: -0.3636363636 + 0.3636363636 = 0.0000000000
0.0000000000 + -0.5454545455x + x2 = 0 + 0.3636363636
-0.5454545455x + x2 = 0 + 0.3636363636

Combine like terms: 0 + 0.3636363636 = 0.3636363636
-0.5454545455x + x2 = 0.3636363636

The x term is -0.5454545455x.  Take half its coefficient (-0.2727272728).
Square it (0.07438016533) and add it to both sides.

Add '0.07438016533' to each side of the equation.
-0.5454545455x + 0.07438016533 + x2 = 0.3636363636 + 0.07438016533

Reorder the terms:
0.07438016533 + -0.5454545455x + x2 = 0.3636363636 + 0.07438016533

Combine like terms: 0.3636363636 + 0.07438016533 = 0.43801652893
0.07438016533 + -0.5454545455x + x2 = 0.43801652893

Factor a perfect square on the left side:
(x + -0.2727272728)(x + -0.2727272728) = 0.43801652893

Calculate the square root of the right side: 0.661828172

Break this problem into two subproblems by setting 
(x + -0.2727272728) equal to 0.661828172 and -0.661828172.

Subproblem 1
x + -0.2727272728 = 0.661828172

Simplifying
x + -0.2727272728 = 0.661828172

Reorder the terms:
-0.2727272728 + x = 0.661828172

Solving
-0.2727272728 + x = 0.661828172

Solving for variable 'x'.

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

Add '0.2727272728' to each side of the equation.
-0.2727272728 + 0.2727272728 + x = 0.661828172 + 0.2727272728

Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000
0.0000000000 + x = 0.661828172 + 0.2727272728
x = 0.661828172 + 0.2727272728

Combine like terms: 0.661828172 + 0.2727272728 = 0.9345554448
x = 0.9345554448

Simplifying
x = 0.9345554448

Subproblem 2
x + -0.2727272728 = -0.661828172

Simplifying
x + -0.2727272728 = -0.661828172

Reorder the terms:
-0.2727272728 + x = -0.661828172

Solving
-0.2727272728 + x = -0.661828172

Solving for variable 'x'.

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

Add '0.2727272728' to each side of the equation.
-0.2727272728 + 0.2727272728 + x = -0.661828172 + 0.2727272728

Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000
0.0000000000 + x = -0.661828172 + 0.2727272728
x = -0.661828172 + 0.2727272728

Combine like terms: -0.661828172 + 0.2727272728 = -0.3891008992
x = -0.3891008992

Simplifying
x = -0.3891008992

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9345554448, -0.3891008992}