16x^2-8x+1=11

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Solution for 16x^2-8x+1=11 equation: 


Simplifying
16x2 + -8x + 1 = 11

Reorder the terms:
1 + -8x + 16x2 = 11

Solving
1 + -8x + 16x2 = 11

Solving for variable 'x'.

Reorder the terms:
1 + -11 + -8x + 16x2 = 11 + -11

Combine like terms: 1 + -11 = -10
-10 + -8x + 16x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-10 + -8x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -4x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + -4x + 8x2)' equal to zero and attempt to solve:

Simplifying
-5 + -4x + 8x2 = 0

Solving
-5 + -4x + 8x2 = 0

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

Divide each side by '8'.
-0.625 + -0.5x + x2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + -0.5x + 0.625 + x2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + -0.5x + x2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + -0.5x + x2 = 0 + 0.625
-0.5x + x2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
-0.5x + x2 = 0.625

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 0.625 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 0.625 + 0.0625

Combine like terms: 0.625 + 0.0625 = 0.6875
0.0625 + -0.5x + x2 = 0.6875

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 0.6875

Calculate the square root of the right side: 0.829156198

Break this problem into two subproblems by setting 
(x + -0.25) equal to 0.829156198 and -0.829156198.


Subproblem 1
x + -0.25 = 0.829156198

Simplifying
x + -0.25 = 0.829156198

Reorder the terms:
-0.25 + x = 0.829156198

Solving
-0.25 + x = 0.829156198

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 0.829156198 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 0.829156198 + 0.25
x = 0.829156198 + 0.25

Combine like terms: 0.829156198 + 0.25 = 1.079156198
x = 1.079156198

Simplifying
x = 1.079156198


Subproblem 2
x + -0.25 = -0.829156198

Simplifying
x + -0.25 = -0.829156198

Reorder the terms:
-0.25 + x = -0.829156198

Solving
-0.25 + x = -0.829156198

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -0.829156198 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -0.829156198 + 0.25
x = -0.829156198 + 0.25

Combine like terms: -0.829156198 + 0.25 = -0.579156198
x = -0.579156198

Simplifying
x = -0.579156198


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.079156198, -0.579156198}
Solution
x = {1.079156198, -0.579156198}

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