2x^2+23x-9.5=0

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Solution for 2x^2+23x-9.5=0 equation: 


Simplifying
2x2 + 23x + -9.5 = 0

Reorder the terms:
-9.5 + 23x + 2x2 = 0

Solving
-9.5 + 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'.
-4.75 + 11.5x + x2 = 0

Move the constant term to the right:

Add '4.75' to each side of the equation.
-4.75 + 11.5x + 4.75 + x2 = 0 + 4.75

Reorder the terms:
-4.75 + 4.75 + 11.5x + x2 = 0 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + 11.5x + x2 = 0 + 4.75
11.5x + x2 = 0 + 4.75

Combine like terms: 0 + 4.75 = 4.75
11.5x + x2 = 4.75

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 = 4.75 + 33.0625

Reorder the terms:
33.0625 + 11.5x + x2 = 4.75 + 33.0625

Combine like terms: 4.75 + 33.0625 = 37.8125
33.0625 + 11.5x + x2 = 37.8125

Factor a perfect square on the left side:
(x + 5.75)(x + 5.75) = 37.8125

Calculate the square root of the right side: 6.149186938

Break this problem into two subproblems by setting 
(x + 5.75) equal to 6.149186938 and -6.149186938.


Subproblem 1
x + 5.75 = 6.149186938

Simplifying
x + 5.75 = 6.149186938

Reorder the terms:
5.75 + x = 6.149186938

Solving
5.75 + x = 6.149186938

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 = 6.149186938 + -5.75

Combine like terms: 5.75 + -5.75 = 0.00
0.00 + x = 6.149186938 + -5.75
x = 6.149186938 + -5.75

Combine like terms: 6.149186938 + -5.75 = 0.399186938
x = 0.399186938

Simplifying
x = 0.399186938


Subproblem 2
x + 5.75 = -6.149186938

Simplifying
x + 5.75 = -6.149186938

Reorder the terms:
5.75 + x = -6.149186938

Solving
5.75 + x = -6.149186938

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 = -6.149186938 + -5.75

Combine like terms: 5.75 + -5.75 = 0.00
0.00 + x = -6.149186938 + -5.75
x = -6.149186938 + -5.75

Combine like terms: -6.149186938 + -5.75 = -11.899186938
x = -11.899186938

Simplifying
x = -11.899186938


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.399186938, -11.899186938}

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