8x^2-52x+4=0

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Solution for 8x^2-52x+4=0 equation: 


Simplifying
8x2 + -52x + 4 = 0

Reorder the terms:
4 + -52x + 8x2 = 0

Solving
4 + -52x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + -13x + 2x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(1 + -13x + 2x2)' equal to zero and attempt to solve:

Simplifying
1 + -13x + 2x2 = 0

Solving
1 + -13x + 2x2 = 0

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

Divide each side by '2'.
0.5 + -6.5x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -6.5x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -6.5x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -6.5x + x2 = 0 + -0.5
-6.5x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-6.5x + x2 = -0.5

The x term is -6.5x.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5x + 10.5625 + x2 = -0.5 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = -0.5 + 10.5625

Combine like terms: -0.5 + 10.5625 = 10.0625
10.5625 + -6.5x + x2 = 10.0625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 10.0625

Calculate the square root of the right side: 3.172144385

Break this problem into two subproblems by setting 
(x + -3.25) equal to 3.172144385 and -3.172144385.


Subproblem 1
x + -3.25 = 3.172144385

Simplifying
x + -3.25 = 3.172144385

Reorder the terms:
-3.25 + x = 3.172144385

Solving
-3.25 + x = 3.172144385

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = 3.172144385 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = 3.172144385 + 3.25
x = 3.172144385 + 3.25

Combine like terms: 3.172144385 + 3.25 = 6.422144385
x = 6.422144385

Simplifying
x = 6.422144385


Subproblem 2
x + -3.25 = -3.172144385

Simplifying
x + -3.25 = -3.172144385

Reorder the terms:
-3.25 + x = -3.172144385

Solving
-3.25 + x = -3.172144385

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = -3.172144385 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = -3.172144385 + 3.25
x = -3.172144385 + 3.25

Combine like terms: -3.172144385 + 3.25 = 0.077855615
x = 0.077855615

Simplifying
x = 0.077855615


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.422144385, 0.077855615}
Solution
x = {6.422144385, 0.077855615}

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