2x^2+17x-6.5=0

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Solution for 2x^2+17x-6.5=0 equation: 


Simplifying
2x2 + 17x + -6.5 = 0

Reorder the terms:
-6.5 + 17x + 2x2 = 0

Solving
-6.5 + 17x + 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'.
-3.25 + 8.5x + x2 = 0

Move the constant term to the right:

Add '3.25' to each side of the equation.
-3.25 + 8.5x + 3.25 + x2 = 0 + 3.25

Reorder the terms:
-3.25 + 3.25 + 8.5x + x2 = 0 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + 8.5x + x2 = 0 + 3.25
8.5x + x2 = 0 + 3.25

Combine like terms: 0 + 3.25 = 3.25
8.5x + x2 = 3.25

The x term is 8.5x.  Take half its coefficient (4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
8.5x + 18.0625 + x2 = 3.25 + 18.0625

Reorder the terms:
18.0625 + 8.5x + x2 = 3.25 + 18.0625

Combine like terms: 3.25 + 18.0625 = 21.3125
18.0625 + 8.5x + x2 = 21.3125

Factor a perfect square on the left side:
(x + 4.25)(x + 4.25) = 21.3125

Calculate the square root of the right side: 4.616546328

Break this problem into two subproblems by setting 
(x + 4.25) equal to 4.616546328 and -4.616546328.


Subproblem 1
x + 4.25 = 4.616546328

Simplifying
x + 4.25 = 4.616546328

Reorder the terms:
4.25 + x = 4.616546328

Solving
4.25 + x = 4.616546328

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4.25' to each side of the equation.
4.25 + -4.25 + x = 4.616546328 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + x = 4.616546328 + -4.25
x = 4.616546328 + -4.25

Combine like terms: 4.616546328 + -4.25 = 0.366546328
x = 0.366546328

Simplifying
x = 0.366546328


Subproblem 2
x + 4.25 = -4.616546328

Simplifying
x + 4.25 = -4.616546328

Reorder the terms:
4.25 + x = -4.616546328

Solving
4.25 + x = -4.616546328

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4.25' to each side of the equation.
4.25 + -4.25 + x = -4.616546328 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + x = -4.616546328 + -4.25
x = -4.616546328 + -4.25

Combine like terms: -4.616546328 + -4.25 = -8.866546328
x = -8.866546328

Simplifying
x = -8.866546328


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.366546328, -8.866546328}

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