2x^2-13x+4.25=0

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Solution for 2x^2-13x+4.25=0 equation: 


Simplifying
2x2 + -13x + 4.25 = 0

Reorder the terms:
4.25 + -13x + 2x2 = 0

Solving
4.25 + -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'.
2.125 + -6.5x + x2 = 0

Move the constant term to the right:

Add '-2.125' to each side of the equation.
2.125 + -6.5x + -2.125 + x2 = 0 + -2.125

Reorder the terms:
2.125 + -2.125 + -6.5x + x2 = 0 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + -6.5x + x2 = 0 + -2.125
-6.5x + x2 = 0 + -2.125

Combine like terms: 0 + -2.125 = -2.125
-6.5x + x2 = -2.125

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 = -2.125 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = -2.125 + 10.5625

Combine like terms: -2.125 + 10.5625 = 8.4375
10.5625 + -6.5x + x2 = 8.4375

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 8.4375

Calculate the square root of the right side: 2.90473751

Break this problem into two subproblems by setting 
(x + -3.25) equal to 2.90473751 and -2.90473751.


Subproblem 1
x + -3.25 = 2.90473751

Simplifying
x + -3.25 = 2.90473751

Reorder the terms:
-3.25 + x = 2.90473751

Solving
-3.25 + x = 2.90473751

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 = 2.90473751 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = 2.90473751 + 3.25
x = 2.90473751 + 3.25

Combine like terms: 2.90473751 + 3.25 = 6.15473751
x = 6.15473751

Simplifying
x = 6.15473751


Subproblem 2
x + -3.25 = -2.90473751

Simplifying
x + -3.25 = -2.90473751

Reorder the terms:
-3.25 + x = -2.90473751

Solving
-3.25 + x = -2.90473751

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 = -2.90473751 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = -2.90473751 + 3.25
x = -2.90473751 + 3.25

Combine like terms: -2.90473751 + 3.25 = 0.34526249
x = 0.34526249

Simplifying
x = 0.34526249


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.15473751, 0.34526249}

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