16x^2-2x-11=0

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Solution for 16x^2-2x-11=0 equation: 


Simplifying
16x2 + -2x + -11 = 0

Reorder the terms:
-11 + -2x + 16x2 = 0

Solving
-11 + -2x + 16x2 = 0

Solving for variable 'x'.

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

Divide each side by '16'.
-0.6875 + -0.125x + x2 = 0

Move the constant term to the right:

Add '0.6875' to each side of the equation.
-0.6875 + -0.125x + 0.6875 + x2 = 0 + 0.6875

Reorder the terms:
-0.6875 + 0.6875 + -0.125x + x2 = 0 + 0.6875

Combine like terms: -0.6875 + 0.6875 = 0.0000
0.0000 + -0.125x + x2 = 0 + 0.6875
-0.125x + x2 = 0 + 0.6875

Combine like terms: 0 + 0.6875 = 0.6875
-0.125x + x2 = 0.6875

The x term is -0.125x.  Take half its coefficient (-0.0625).
Square it (0.00390625) and add it to both sides.

Add '0.00390625' to each side of the equation.
-0.125x + 0.00390625 + x2 = 0.6875 + 0.00390625

Reorder the terms:
0.00390625 + -0.125x + x2 = 0.6875 + 0.00390625

Combine like terms: 0.6875 + 0.00390625 = 0.69140625
0.00390625 + -0.125x + x2 = 0.69140625

Factor a perfect square on the left side:
(x + -0.0625)(x + -0.0625) = 0.69140625

Calculate the square root of the right side: 0.831508418

Break this problem into two subproblems by setting 
(x + -0.0625) equal to 0.831508418 and -0.831508418.


Subproblem 1
x + -0.0625 = 0.831508418

Simplifying
x + -0.0625 = 0.831508418

Reorder the terms:
-0.0625 + x = 0.831508418

Solving
-0.0625 + x = 0.831508418

Solving for variable 'x'.

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

Add '0.0625' to each side of the equation.
-0.0625 + 0.0625 + x = 0.831508418 + 0.0625

Combine like terms: -0.0625 + 0.0625 = 0.0000
0.0000 + x = 0.831508418 + 0.0625
x = 0.831508418 + 0.0625

Combine like terms: 0.831508418 + 0.0625 = 0.894008418
x = 0.894008418

Simplifying
x = 0.894008418


Subproblem 2
x + -0.0625 = -0.831508418

Simplifying
x + -0.0625 = -0.831508418

Reorder the terms:
-0.0625 + x = -0.831508418

Solving
-0.0625 + x = -0.831508418

Solving for variable 'x'.

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

Add '0.0625' to each side of the equation.
-0.0625 + 0.0625 + x = -0.831508418 + 0.0625

Combine like terms: -0.0625 + 0.0625 = 0.0000
0.0000 + x = -0.831508418 + 0.0625
x = -0.831508418 + 0.0625

Combine like terms: -0.831508418 + 0.0625 = -0.769008418
x = -0.769008418

Simplifying
x = -0.769008418


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.894008418, -0.769008418}

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