2x^2-26x+16=0

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Solution for 2x^2-26x+16=0 equation: 


Simplifying
2x2 + -26x + 16 = 0

Reorder the terms:
16 + -26x + 2x2 = 0

Solving
16 + -26x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -13x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8 + -13x + x2)' equal to zero and attempt to solve:

Simplifying
8 + -13x + x2 = 0

Solving
8 + -13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -13x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -13x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -13x + x2 = 0 + -8
-13x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-13x + x2 = -8

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = -8 + 42.25

Reorder the terms:
42.25 + -13x + x2 = -8 + 42.25

Combine like terms: -8 + 42.25 = 34.25
42.25 + -13x + x2 = 34.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 34.25

Calculate the square root of the right side: 5.852349955

Break this problem into two subproblems by setting 
(x + -6.5) equal to 5.852349955 and -5.852349955.


Subproblem 1
x + -6.5 = 5.852349955

Simplifying
x + -6.5 = 5.852349955

Reorder the terms:
-6.5 + x = 5.852349955

Solving
-6.5 + x = 5.852349955

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = 5.852349955 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 5.852349955 + 6.5
x = 5.852349955 + 6.5

Combine like terms: 5.852349955 + 6.5 = 12.352349955
x = 12.352349955

Simplifying
x = 12.352349955


Subproblem 2
x + -6.5 = -5.852349955

Simplifying
x + -6.5 = -5.852349955

Reorder the terms:
-6.5 + x = -5.852349955

Solving
-6.5 + x = -5.852349955

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = -5.852349955 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = -5.852349955 + 6.5
x = -5.852349955 + 6.5

Combine like terms: -5.852349955 + 6.5 = 0.647650045
x = 0.647650045

Simplifying
x = 0.647650045


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.352349955, 0.647650045}
Solution
x = {12.352349955, 0.647650045}

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