2x^2-20x+16-8x=0

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Solution for 2x^2-20x+16-8x=0 equation: 


Simplifying
2x2 + -20x + 16 + -8x = 0

Reorder the terms:
16 + -20x + -8x + 2x2 = 0

Combine like terms: -20x + -8x = -28x
16 + -28x + 2x2 = 0

Solving
16 + -28x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -14x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8 + -14x + x2)' equal to zero and attempt to solve:

Simplifying
8 + -14x + x2 = 0

Solving
8 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -14x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -14x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -14x + x2 = 0 + -8
-14x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-14x + x2 = -8

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = -8 + 49

Reorder the terms:
49 + -14x + x2 = -8 + 49

Combine like terms: -8 + 49 = 41
49 + -14x + x2 = 41

Factor a perfect square on the left side:
(x + -7)(x + -7) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(x + -7) equal to 6.403124237 and -6.403124237.


Subproblem 1
x + -7 = 6.403124237

Simplifying
x + -7 = 6.403124237

Reorder the terms:
-7 + x = 6.403124237

Solving
-7 + x = 6.403124237

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 6.403124237 + 7

Combine like terms: -7 + 7 = 0
0 + x = 6.403124237 + 7
x = 6.403124237 + 7

Combine like terms: 6.403124237 + 7 = 13.403124237
x = 13.403124237

Simplifying
x = 13.403124237


Subproblem 2
x + -7 = -6.403124237

Simplifying
x + -7 = -6.403124237

Reorder the terms:
-7 + x = -6.403124237

Solving
-7 + x = -6.403124237

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -6.403124237 + 7

Combine like terms: -7 + 7 = 0
0 + x = -6.403124237 + 7
x = -6.403124237 + 7

Combine like terms: -6.403124237 + 7 = 0.596875763
x = 0.596875763

Simplifying
x = 0.596875763


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.403124237, 0.596875763}
Solution
x = {13.403124237, 0.596875763}

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