2x^2-13x-6=0

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Solution for 2x^2-13x-6=0 equation:


Simplifying
2x2 + -13x + -6 = 0

Reorder the terms:
-6 + -13x + 2x2 = 0

Solving
-6 + -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'.
-3 + -6.5x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -6.5x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -6.5x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -6.5x + x2 = 0 + 3
-6.5x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-6.5x + x2 = 3

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 = 3 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = 3 + 10.5625

Combine like terms: 3 + 10.5625 = 13.5625
10.5625 + -6.5x + x2 = 13.5625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 13.5625

Calculate the square root of the right side: 3.682729966

Break this problem into two subproblems by setting 
(x + -3.25) equal to 3.682729966 and -3.682729966.

Subproblem 1

x + -3.25 = 3.682729966 Simplifying x + -3.25 = 3.682729966 Reorder the terms: -3.25 + x = 3.682729966 Solving -3.25 + x = 3.682729966 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 = 3.682729966 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 3.682729966 + 3.25 x = 3.682729966 + 3.25 Combine like terms: 3.682729966 + 3.25 = 6.932729966 x = 6.932729966 Simplifying x = 6.932729966

Subproblem 2

x + -3.25 = -3.682729966 Simplifying x + -3.25 = -3.682729966 Reorder the terms: -3.25 + x = -3.682729966 Solving -3.25 + x = -3.682729966 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 = -3.682729966 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -3.682729966 + 3.25 x = -3.682729966 + 3.25 Combine like terms: -3.682729966 + 3.25 = -0.432729966 x = -0.432729966 Simplifying x = -0.432729966

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.932729966, -0.432729966}

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