(x^2)-19x+9.5=0

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Solution for (x^2)-19x+9.5=0 equation: 


Simplifying
(x2) + -19x + 9.5 = 0
x2 + -19x + 9.5 = 0

Reorder the terms:
9.5 + -19x + x2 = 0

Solving
9.5 + -19x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-9.5' to each side of the equation.
9.5 + -19x + -9.5 + x2 = 0 + -9.5

Reorder the terms:
9.5 + -9.5 + -19x + x2 = 0 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + -19x + x2 = 0 + -9.5
-19x + x2 = 0 + -9.5

Combine like terms: 0 + -9.5 = -9.5
-19x + x2 = -9.5

The x term is -19x.  Take half its coefficient (-9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
-19x + 90.25 + x2 = -9.5 + 90.25

Reorder the terms:
90.25 + -19x + x2 = -9.5 + 90.25

Combine like terms: -9.5 + 90.25 = 80.75
90.25 + -19x + x2 = 80.75

Factor a perfect square on the left side:
(x + -9.5)(x + -9.5) = 80.75

Calculate the square root of the right side: 8.986100378

Break this problem into two subproblems by setting 
(x + -9.5) equal to 8.986100378 and -8.986100378.


Subproblem 1
x + -9.5 = 8.986100378

Simplifying
x + -9.5 = 8.986100378

Reorder the terms:
-9.5 + x = 8.986100378

Solving
-9.5 + x = 8.986100378

Solving for variable 'x'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + x = 8.986100378 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x = 8.986100378 + 9.5
x = 8.986100378 + 9.5

Combine like terms: 8.986100378 + 9.5 = 18.486100378
x = 18.486100378

Simplifying
x = 18.486100378


Subproblem 2
x + -9.5 = -8.986100378

Simplifying
x + -9.5 = -8.986100378

Reorder the terms:
-9.5 + x = -8.986100378

Solving
-9.5 + x = -8.986100378

Solving for variable 'x'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + x = -8.986100378 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x = -8.986100378 + 9.5
x = -8.986100378 + 9.5

Combine like terms: -8.986100378 + 9.5 = 0.513899622
x = 0.513899622

Simplifying
x = 0.513899622


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.486100378, 0.513899622}

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