x^2-9.5x-5=0

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Solution for x^2-9.5x-5=0 equation: 


Simplifying
x2 + -9.5x + -5 = 0

Reorder the terms:
-5 + -9.5x + x2 = 0

Solving
-5 + -9.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -9.5x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -9.5x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -9.5x + x2 = 0 + 5
-9.5x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-9.5x + x2 = 5

The x term is -9.5x.  Take half its coefficient (-4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
-9.5x + 22.5625 + x2 = 5 + 22.5625

Reorder the terms:
22.5625 + -9.5x + x2 = 5 + 22.5625

Combine like terms: 5 + 22.5625 = 27.5625
22.5625 + -9.5x + x2 = 27.5625

Factor a perfect square on the left side:
(x + -4.75)(x + -4.75) = 27.5625

Calculate the square root of the right side: 5.25

Break this problem into two subproblems by setting 
(x + -4.75) equal to 5.25 and -5.25.


Subproblem 1
x + -4.75 = 5.25

Simplifying
x + -4.75 = 5.25

Reorder the terms:
-4.75 + x = 5.25

Solving
-4.75 + x = 5.25

Solving for variable 'x'.

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

Add '4.75' to each side of the equation.
-4.75 + 4.75 + x = 5.25 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + x = 5.25 + 4.75
x = 5.25 + 4.75

Combine like terms: 5.25 + 4.75 = 10
x = 10

Simplifying
x = 10


Subproblem 2
x + -4.75 = -5.25

Simplifying
x + -4.75 = -5.25

Reorder the terms:
-4.75 + x = -5.25

Solving
-4.75 + x = -5.25

Solving for variable 'x'.

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

Add '4.75' to each side of the equation.
-4.75 + 4.75 + x = -5.25 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + x = -5.25 + 4.75
x = -5.25 + 4.75

Combine like terms: -5.25 + 4.75 = -0.5
x = -0.5

Simplifying
x = -0.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10, -0.5}

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