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 = 99.75
90.25 + -19x + x2 = 99.75

Factor a perfect square on the left side:
(x + -9.5)(x + -9.5) = 99.75

Calculate the square root of the right side: 9.987492178

Break this problem into two subproblems by setting 
(x + -9.5) equal to 9.987492178 and -9.987492178.


Subproblem 1
x + -9.5 = 9.987492178

Simplifying
x + -9.5 = 9.987492178

Reorder the terms:
-9.5 + x = 9.987492178

Solving
-9.5 + x = 9.987492178

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 = 9.987492178 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x = 9.987492178 + 9.5
x = 9.987492178 + 9.5

Combine like terms: 9.987492178 + 9.5 = 19.487492178
x = 19.487492178

Simplifying
x = 19.487492178


Subproblem 2
x + -9.5 = -9.987492178

Simplifying
x + -9.5 = -9.987492178

Reorder the terms:
-9.5 + x = -9.987492178

Solving
-9.5 + x = -9.987492178

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 = -9.987492178 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x = -9.987492178 + 9.5
x = -9.987492178 + 9.5

Combine like terms: -9.987492178 + 9.5 = -0.487492178
x = -0.487492178

Simplifying
x = -0.487492178


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.487492178, -0.487492178}

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