x^2-19x+16=0

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


Simplifying
x2 + -19x + 16 = 0

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

Solving
16 + -19x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -16 + 90.25

Reorder the terms:
90.25 + -19x + x2 = -16 + 90.25

Combine like terms: -16 + 90.25 = 74.25
90.25 + -19x + x2 = 74.25

Factor a perfect square on the left side:
(x + -9.5)(x + -9.5) = 74.25

Calculate the square root of the right side: 8.61684397

Break this problem into two subproblems by setting 
(x + -9.5) equal to 8.61684397 and -8.61684397.


Subproblem 1
x + -9.5 = 8.61684397

Simplifying
x + -9.5 = 8.61684397

Reorder the terms:
-9.5 + x = 8.61684397

Solving
-9.5 + x = 8.61684397

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 = 8.61684397 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x = 8.61684397 + 9.5
x = 8.61684397 + 9.5

Combine like terms: 8.61684397 + 9.5 = 18.11684397
x = 18.11684397

Simplifying
x = 18.11684397


Subproblem 2
x + -9.5 = -8.61684397

Simplifying
x + -9.5 = -8.61684397

Reorder the terms:
-9.5 + x = -8.61684397

Solving
-9.5 + x = -8.61684397

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 = -8.61684397 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x = -8.61684397 + 9.5
x = -8.61684397 + 9.5

Combine like terms: -8.61684397 + 9.5 = 0.88315603
x = 0.88315603

Simplifying
x = 0.88315603


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.11684397, 0.88315603}

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