2x^2-13x+1=0

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Solution for 2x^2-13x+1=0 equation:


Simplifying
2x2 + -13x + 1 = 0

Reorder the terms:
1 + -13x + 2x2 = 0

Solving
1 + -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'.
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}

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