2x^2+23x-6.5=0

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Solution for 2x^2+23x-6.5=0 equation: 


Simplifying
2x2 + 23x + -6.5 = 0

Reorder the terms:
-6.5 + 23x + 2x2 = 0

Solving
-6.5 + 23x + 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 + 11.5x + x2 = 0

Move the constant term to the right:

Add '3.25' to each side of the equation.
-3.25 + 11.5x + 3.25 + x2 = 0 + 3.25

Reorder the terms:
-3.25 + 3.25 + 11.5x + x2 = 0 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + 11.5x + x2 = 0 + 3.25
11.5x + x2 = 0 + 3.25

Combine like terms: 0 + 3.25 = 3.25
11.5x + x2 = 3.25

The x term is 11.5x.  Take half its coefficient (5.75).
Square it (33.0625) and add it to both sides.

Add '33.0625' to each side of the equation.
11.5x + 33.0625 + x2 = 3.25 + 33.0625

Reorder the terms:
33.0625 + 11.5x + x2 = 3.25 + 33.0625

Combine like terms: 3.25 + 33.0625 = 36.3125
33.0625 + 11.5x + x2 = 36.3125

Factor a perfect square on the left side:
(x + 5.75)(x + 5.75) = 36.3125

Calculate the square root of the right side: 6.025985397

Break this problem into two subproblems by setting 
(x + 5.75) equal to 6.025985397 and -6.025985397.


Subproblem 1
x + 5.75 = 6.025985397

Simplifying
x + 5.75 = 6.025985397

Reorder the terms:
5.75 + x = 6.025985397

Solving
5.75 + x = 6.025985397

Solving for variable 'x'.

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

Add '-5.75' to each side of the equation.
5.75 + -5.75 + x = 6.025985397 + -5.75

Combine like terms: 5.75 + -5.75 = 0.00
0.00 + x = 6.025985397 + -5.75
x = 6.025985397 + -5.75

Combine like terms: 6.025985397 + -5.75 = 0.275985397
x = 0.275985397

Simplifying
x = 0.275985397


Subproblem 2
x + 5.75 = -6.025985397

Simplifying
x + 5.75 = -6.025985397

Reorder the terms:
5.75 + x = -6.025985397

Solving
5.75 + x = -6.025985397

Solving for variable 'x'.

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

Add '-5.75' to each side of the equation.
5.75 + -5.75 + x = -6.025985397 + -5.75

Combine like terms: 5.75 + -5.75 = 0.00
0.00 + x = -6.025985397 + -5.75
x = -6.025985397 + -5.75

Combine like terms: -6.025985397 + -5.75 = -11.775985397
x = -11.775985397

Simplifying
x = -11.775985397


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.275985397, -11.775985397}

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