2x^2-13x+5=0

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Solution for 2x^2-13x+5=0 equation: 


Simplifying
2x2 + -13x + 5 = 0

Reorder the terms:
5 + -13x + 2x2 = 0

Solving
5 + -13x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
2.5 + -6.5x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -6.5x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -6.5x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -6.5x + x2 = 0 + -2.5
-6.5x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-6.5x + x2 = -2.5

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 = -2.5 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = -2.5 + 10.5625

Combine like terms: -2.5 + 10.5625 = 8.0625
10.5625 + -6.5x + x2 = 8.0625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 8.0625

Calculate the square root of the right side: 2.839454173

Break this problem into two subproblems by setting 
(x + -3.25) equal to 2.839454173 and -2.839454173.


Subproblem 1
x + -3.25 = 2.839454173

Simplifying
x + -3.25 = 2.839454173

Reorder the terms:
-3.25 + x = 2.839454173

Solving
-3.25 + x = 2.839454173

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 = 2.839454173 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = 2.839454173 + 3.25
x = 2.839454173 + 3.25

Combine like terms: 2.839454173 + 3.25 = 6.089454173
x = 6.089454173

Simplifying
x = 6.089454173


Subproblem 2
x + -3.25 = -2.839454173

Simplifying
x + -3.25 = -2.839454173

Reorder the terms:
-3.25 + x = -2.839454173

Solving
-3.25 + x = -2.839454173

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 = -2.839454173 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = -2.839454173 + 3.25
x = -2.839454173 + 3.25

Combine like terms: -2.839454173 + 3.25 = 0.410545827
x = 0.410545827

Simplifying
x = 0.410545827


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.089454173, 0.410545827}

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