x^2-16x-19=0

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Solution for x^2-16x-19=0 equation:


Simplifying
x2 + -16x + -19 = 0

Reorder the terms:
-19 + -16x + x2 = 0

Solving
-19 + -16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + -16x + 19 + x2 = 0 + 19

Reorder the terms:
-19 + 19 + -16x + x2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -16x + x2 = 0 + 19
-16x + x2 = 0 + 19

Combine like terms: 0 + 19 = 19
-16x + x2 = 19

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = 19 + 64

Reorder the terms:
64 + -16x + x2 = 19 + 64

Combine like terms: 19 + 64 = 83
64 + -16x + x2 = 83

Factor a perfect square on the left side:
(x + -8)(x + -8) = 83

Calculate the square root of the right side: 9.110433579

Break this problem into two subproblems by setting 
(x + -8) equal to 9.110433579 and -9.110433579.


Subproblem 1
x + -8 = 9.110433579

Simplifying
x + -8 = 9.110433579

Reorder the terms:
-8 + x = 9.110433579

Solving
-8 + x = 9.110433579

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = 9.110433579 + 8

Combine like terms: -8 + 8 = 0
0 + x = 9.110433579 + 8
x = 9.110433579 + 8

Combine like terms: 9.110433579 + 8 = 17.110433579
x = 17.110433579

Simplifying
x = 17.110433579


Subproblem 2
x + -8 = -9.110433579

Simplifying
x + -8 = -9.110433579

Reorder the terms:
-8 + x = -9.110433579

Solving
-8 + x = -9.110433579

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = -9.110433579 + 8

Combine like terms: -8 + 8 = 0
0 + x = -9.110433579 + 8
x = -9.110433579 + 8

Combine like terms: -9.110433579 + 8 = -1.110433579
x = -1.110433579

Simplifying
x = -1.110433579


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.110433579, -1.110433579}

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