0=2x^2-13x-1

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


Simplifying
0 = 2x2 + -13x + -1

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

Solving
0 = -1 + -13x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 1 = 1
1 + 13x + -2x2 = -1 + -13x + 2x2 + 1 + 13x + -2x2

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

Combine like terms: -1 + 1 = 0
1 + 13x + -2x2 = 0 + -13x + 13x + 2x2 + -2x2
1 + 13x + -2x2 = -13x + 13x + 2x2 + -2x2

Combine like terms: -13x + 13x = 0
1 + 13x + -2x2 = 0 + 2x2 + -2x2
1 + 13x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
1 + 13x + -2x2 = 0

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 = 11.0625
10.5625 + -6.5x + x2 = 11.0625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 11.0625

Calculate the square root of the right side: 3.326033674

Break this problem into two subproblems by setting 
(x + -3.25) equal to 3.326033674 and -3.326033674.

Subproblem 1

x + -3.25 = 3.326033674 Simplifying x + -3.25 = 3.326033674 Reorder the terms: -3.25 + x = 3.326033674 Solving -3.25 + x = 3.326033674 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 = 3.326033674 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 3.326033674 + 3.25 x = 3.326033674 + 3.25 Combine like terms: 3.326033674 + 3.25 = 6.576033674 x = 6.576033674 Simplifying x = 6.576033674

Subproblem 2

x + -3.25 = -3.326033674 Simplifying x + -3.25 = -3.326033674 Reorder the terms: -3.25 + x = -3.326033674 Solving -3.25 + x = -3.326033674 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 = -3.326033674 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -3.326033674 + 3.25 x = -3.326033674 + 3.25 Combine like terms: -3.326033674 + 3.25 = -0.076033674 x = -0.076033674 Simplifying x = -0.076033674

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.576033674, -0.076033674}

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