2x^2-1x-13=0

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


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

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

Solving
-13 + -1x + 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'.
-6.5 + -0.5x + x2 = 0

Move the constant term to the right:

Add '6.5' to each side of the equation.
-6.5 + -0.5x + 6.5 + x2 = 0 + 6.5

Reorder the terms:
-6.5 + 6.5 + -0.5x + x2 = 0 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + -0.5x + x2 = 0 + 6.5
-0.5x + x2 = 0 + 6.5

Combine like terms: 0 + 6.5 = 6.5
-0.5x + x2 = 6.5

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 6.5 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 6.5 + 0.0625

Combine like terms: 6.5 + 0.0625 = 6.5625
0.0625 + -0.5x + x2 = 6.5625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 6.5625

Calculate the square root of the right side: 2.561737691

Break this problem into two subproblems by setting 
(x + -0.25) equal to 2.561737691 and -2.561737691.

Subproblem 1

x + -0.25 = 2.561737691 Simplifying x + -0.25 = 2.561737691 Reorder the terms: -0.25 + x = 2.561737691 Solving -0.25 + x = 2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 2.561737691 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.561737691 + 0.25 x = 2.561737691 + 0.25 Combine like terms: 2.561737691 + 0.25 = 2.811737691 x = 2.811737691 Simplifying x = 2.811737691

Subproblem 2

x + -0.25 = -2.561737691 Simplifying x + -0.25 = -2.561737691 Reorder the terms: -0.25 + x = -2.561737691 Solving -0.25 + x = -2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -2.561737691 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.561737691 + 0.25 x = -2.561737691 + 0.25 Combine like terms: -2.561737691 + 0.25 = -2.311737691 x = -2.311737691 Simplifying x = -2.311737691

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.811737691, -2.311737691}

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